# It's a trigonometric dilemma

Geometry Level 4

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

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 $$\sin x$$?

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