Question 57
In the real numbers, solve the following system of equations:
$$
\begin{aligned}
\sin^2 x + \cos^2 y &= \tan^2 z, \\
\sin^2 y + \cos^2 z &= \tan^2 x, \\
\sin^2 z + \cos^2 x &= \tan^2 y.
\end{aligned}
$$
$$
\begin{aligned}
\sin^2 x + \cos^2 y &= \tan^2 z, \\
\sin^2 y + \cos^2 z &= \tan^2 x, \\
\sin^2 z + \cos^2 x &= \tan^2 y.
\end{aligned}
$$