Equations system 1

Solve the system :
$$\begin{gathered} \frac{4x^2}{1+4x^2}=y \\ \frac{4y^2}{1+4y^2}=z \\ \frac{4z^2}{1+4z^2}=x \end{gathered}$$
$\text{with }x,y,z\ne 0$

Answer format: x,y,z (in form p/q as they are rational numbers)