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I think you are right about the fact that you found a bug, which is unfortunately not rare when working in the Symbolic Ring :/ Could you report it on the trac server by yourself (ask for help in comment otherwise) ?

A way to get the correct solution, though not satisfactory, is to simplify the expression zi first, to help the solver:

sage: zzi = zi.full_simplify()
sage: zzi
-cos(phi)/(sqrt(2)*sin(phi) + sqrt(2))

sage: solve(zzi == 0, phi)
[phi == 1/2*pi]

This both gives you the correct answer and confirms that your hand-made calculation is reliable :)

I think you are right about the fact that you found This is indeed a bug, which is unfortunately not rare when working in the Symbolic Ring :/ Could you report it on the trac server by yourself (ask for help in comment otherwise) ?

A way to get the correct solution, though not satisfactory, is to simplify the expression zi first, to help the solver:

sage: zzi = zi.full_simplify()
sage: zzi
-cos(phi)/(sqrt(2)*sin(phi) + sqrt(2))

sage: solve(zzi == 0, phi)
[phi == 1/2*pi]

This both gives you the correct answer and confirms that your hand-made calculation is reliable :)