It's a trigonometric dilemma

$\large \begin{cases} \cos x =\tan y \\ \cos y = \tan z \\ \cos z =\tan x \end{cases}$

If $x, y$ and $z$ are real numbers that satisfy the above system of equations with $0 \leq \sin x \leq 1$ , then what is the value of $\sin x$ ?