# Zero solution does not result in zero

The following looks like a bug to me, but I would value a second opinion:

```
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| Sage Version 5.8, Release Date: 2013-03-15 |
| Type "notebook()" for the browser-based notebook interface. |
| Type "help()" for help. |
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sage: phi = var('phi', domain='real')
sage: M = Matrix([
....: [-sqrt(-I)/(exp(I*phi)-1), sqrt(-I)/(exp(I*phi)-1)],
....: [-1/(exp(I*phi)-1)+exp(-I*phi), 1/(exp(I*phi)-1)]])
sage: z = M*vector((-I, 1))
sage: z = z[0]/z[1]
sage: zi = z.imag_part()
sage: s1 = [s.rhs() for s in solve(zi == 0, phi)]
sage: s1
[0, pi - arccos(1/2*sqrt(5) - 1/2), arccos(1/2*sqrt(5) + 1/2)]
sage: N(zi.subs(phi=s1[1]))
0.244669085661435
sage: zi.subs(phi=pi/2)
0
```

So the solutions *should* result in a zero of the `zi`

expression, but apparently that is not the case. Instead, some value which is *not* listed among the solutions turns out to be a solution. Did I make some mistake here, or is this a bug in sage?

*Edit:* `zi`

should be equal to `-1/2*sqrt(2)*cos(phi)/(sin(phi) + 1)`

.
This is the expression from which I eventually derived the correct solution.