Solve the following system of equations:

\frac{2x_{1}^{2}}{1+x_{1}^{2}} = x_{2},
\frac{2x_{2}^{2}}{1+x_{2}^{2}} = x_{3},
\frac{2x_{3}^{2}}{1+x_{3}^{2}} = x_{1}.

Solution