# Don't Just answer, Prove it!

Algebra Level pending

$\large x=\frac{2z^2}{1+z^2} \qquad y=\frac{2x^2}{1+x^2} \qquad z=\frac{2y^2}{1+y^2}$

Let real numbers $$x$$, $$y$$ and $$z$$ satisfy the system of equations above. Find the number of real solutions not including the trivial solution $$(0,0,0)$$.

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