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Here in an example that can be run at Sagecell. It produces the result in the form of a LaTeX file:

f = cos(2*pi/17).minpoly()
gap.eval('LoadPackage("radiroot");')
gap.eval(f'x := Indeterminate( Rationals, "{f.variables()[0]}" );')
print('Solvable:', gap.eval(f'IsSolvablePolynomial({f});') )
fname = gap.eval(f'RootsOfPolynomialAsRadicals( {f}, "latex" );')
with open(fname) as file:
    for line in file:
        print(fr'{line.rstrip()}')

Here in an example that can be run at Sagecell. Sagecell for $n=5$ and $n=17$. It produces the result in the form of a LaTeX file:file. For $n=257$, it gives an error Transitive groups of degree 128 are not available.

n = 5
f = cos(2*pi/17).minpoly()
cos(2*pi/n).minpoly()
gap.eval('LoadPackage("radiroot");')
gap.eval(f'x := Indeterminate( Rationals, "{f.variables()[0]}" );')
print('Solvable:', gap.eval(f'IsSolvablePolynomial({f});') )
assert gap.eval(f'IsSolvablePolynomial({f});')
fname = gap.eval(f'RootsOfPolynomialAsRadicals( {f}, "latex" );')
with open(fname) as file:
try:
 file = open(fname)
except:
    file = open(eval(fname))
for line in file:
     print(fr'{line.rstrip()}')

Here in an example that can be run at Sagecell for $n=5$ and $n=17$. It produces the result in the form of a LaTeX file. For $n=257$, it gives an error Transitive groups of degree 128 are not available.

n = 5
f = cos(2*pi/n).minpoly()
gap.eval('LoadPackage("radiroot");')
gap.eval(f'x := Indeterminate( Rationals, "{f.variables()[0]}" );')
assert gap.eval(f'IsSolvablePolynomial({f});')
gap.eval(f'IsSolvablePolynomial({f});')     # necessary condition
fname = gap.eval(f'RootsOfPolynomialAsRadicals( {f}, "latex" );')
try:
);').strip('"')
with open(fname) as file:
 file = open(fname)
except:
    file = open(eval(fname))
for line in file:
     print(fr'{line.rstrip()}')

Here in an example that can be run at Sagecell for $n=5$ and $n=17$. $n=17$ using GAP's RadiRoot package. It produces the result in the form of a LaTeX file. For $n=257$, it gives an error Transitive groups of degree 128 are not available.

n = 5
f = cos(2*pi/n).minpoly()
gap.eval('LoadPackage("radiroot");')
gap.eval(f'x := Indeterminate( Rationals, "{f.variables()[0]}" );')
assert gap.eval(f'IsSolvablePolynomial({f});')     # necessary condition
fname = gap.eval(f'RootsOfPolynomialAsRadicals( {f}, "latex" );').strip('"')
with open(fname) as file:
    for line in file:
        print(fr'{line.rstrip()}')

Here in an example that can be run at Sagecell for $n=5$ and $n=17$ a sample code using GAP's RadiRoot package. that works for $n=5$ and $n=17$. It produces the result in the form of a LaTeX file. For $n=257$, it gives an error Transitive groups of degree 128 are not available., while for $n=65537$ it goes into lengthy calculations (I was not patient enough to wait for an answer).

n = 5
f = cos(2*pi/n).minpoly()
gap.eval('LoadPackage("radiroot");')
gap.eval(f'x := Indeterminate( Rationals, "{f.variables()[0]}" );')
assert gap.eval(f'IsSolvablePolynomial({f});')     # necessary condition
fname = gap.eval(f'RootsOfPolynomialAsRadicals( {f}, "latex" );').strip('"')
with open(fname) as file:
    for line in file:
        print(fr'{line.rstrip()}')

Here in a sample code using GAP's RadiRoot package that works for $n=5$ and $n=17$. It produces the result in the form of a LaTeX file. For $n=257$, it gives an error Transitive groups of degree 128 are not available, while for $n=65537$ it goes into lengthy calculations (I was not patient enough to wait for an answer).

n = 5
f = cos(2*pi/n).minpoly()
gap.eval('LoadPackage("radiroot");')
gap.eval(f'x := Indeterminate( Rationals, "{f.variables()[0]}" "{f.variable_name()}" );')
assert gap.eval(f'IsSolvablePolynomial({f});')     # necessary condition
fname = gap.eval(f'RootsOfPolynomialAsRadicals( {f}, "latex" );').strip('"')
with open(fname) as file:
    for line in file:
        print(fr'{line.rstrip()}')

Here in a sample code using GAP's RadiRoot package that works for $n=5$ and $n=17$. It produces the result in the form of a LaTeX file. For $n=257$, it gives an error Transitive groups of degree 128 are not available, while for $n=65537$ it goes into lengthy calculations (I was not patient enough to wait for an answer).

n = 5
f = cos(2*pi/n).minpoly()
x = f.variables()[0]
gap.eval('LoadPackage("radiroot");')
gap.eval(f'x gap.eval(f'{x} := Indeterminate( Rationals, "{f.variable_name()}" "{x}" );')
assert gap.eval(f'IsSolvablePolynomial({f});')     # necessary condition
fname = gap.eval(f'RootsOfPolynomialAsRadicals( {f}, "latex" );').strip('"')
with open(fname) as file:
    for line in file:
        print(fr'{line.rstrip()}')