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Here is a solution for the "same" problem, designed but as i would design the process:

• it is natural to separate the in and out file, thus not write in the same file. (Hard to test, some users will hate this overwriting behavior, if not really attentioned, this is also the best way to loose data when errors in coding occur.)
• the outfile will have & as separator, so that i may try to insert the result in there...
• no csv (reader) import will be done to keep things simple.

Code:

import traceback

SEPARATOR     = ';'          # or ',' or ' & ' or ...
SEPARATOR_IN  = ';'          # or ',' or ' & ' or ...
SEPARATOR_OUT = '\n    &'    # or ',' or ' & ' or ...
END_OUT       = '\\\\\n'     # or simply '\n'

inFileName  = r"/home/dan/temp/in1234.csv"
outFileName = r"/home/dan/temp/out1234.csv"

def f(u):
    return latex( sin( u/180 *pi ) )

def printOut( x,y, outStream, sep=SEPARATOR ):
    z = x+y
    outList = [ r"%s^\circ" % x ,
                r"%s^\circ" % y ,
                r"%s^\circ" % z ,
                f(x) ,
                f(y) ,
                f(z) , ]

    outStream.write( sep.join( [ str(entry) for entry in outList ] ) + END_OUT )

inStream  = open(  inFileName, 'r' )    # open for read
outStream = open( outFileName, 'w' )    # open for write

for line in inStream:
    print "... parsing %s" % line
    try:
        x, y = line.strip().split( SEPARATOR_IN )[:2]
        x, y = ZZ(x), ZZ(y)
        printOut( x, y, outStream, sep=SEPARATOR_OUT )
    except Exception:
        traceback.print_exc()

inStream.close()
outStream.close()

Use corresponding separators for the own needs. My input file has the lines:

15;30
12;24
30;45
60;90
72;120
6;18;

and i use the German separator, the semicolon. Redefine the separator(s) for the own needs. The output is like this, rather designed to be inserted into a latex document, inside of an array block:

15^\circ
    &30^\circ
    &45^\circ
    &\frac{1}{4} \, \sqrt{6} - \frac{1}{4} \, \sqrt{2}
    &\frac{1}{2}
    &\frac{1}{2} \, \sqrt{2}\\
12^\circ
    &24^\circ
    &36^\circ
    &\sin\left(\frac{1}{15} \, \pi\right)
    &\sin\left(\frac{2}{15} \, \pi\right)
    &\frac{1}{4} \, \sqrt{-2 \, \sqrt{5} + 10}\\
30^\circ
    &45^\circ
    &75^\circ
    &\frac{1}{2}
    &\frac{1}{2} \, \sqrt{2}
    &\frac{1}{4} \, \sqrt{6} + \frac{1}{4} \, \sqrt{2}\\
60^\circ
    &90^\circ
    &150^\circ
    &\frac{1}{2} \, \sqrt{3}
    &1
    &\frac{1}{2}\\
72^\circ
    &120^\circ
    &192^\circ
    &\frac{1}{4} \, \sqrt{2 \, \sqrt{5} + 10}
    &\frac{1}{2} \, \sqrt{3}
    &-\sin\left(\frac{1}{15} \, \pi\right)\\

The columns correspond to $x,y,x+y$ and then we apply the sine on these values one by one. If you insist to give the formulas in the header of the in-File, then you have to parse and eval them.

Note: In order to also get something out of $\sin(\pi/15)$ one may use:

def g(u):

    roots = [ r
              for r in u.minpoly(X).roots(ring=AA, multiplicities=False )
              if abs( r-u.n() ) < 0.0001 ]
    if roots:
        r = roots[0]
        return r.radical_expression()
    return '?'

when

sage: latex( g( sin( pi/15 ) ) )
\frac{1}{4} \, \sqrt{-\sqrt{5} - 8 \, \sqrt{-\frac{3}{32} \, \sqrt{5} + \frac{15}{32}} + 7}

delivers $$ \frac{1}{4} \, \sqrt{-\sqrt{5} - 8 \, \sqrt{-\frac{3}{32} \, \sqrt{5} + \frac{15}{32}} + 7}\ .$$ (Not the best shape for a human, but a result.)