Can you please help me solve this system of equations (frankly I have no idea, it's the first equation of this type that I solve, so please, write only a hint):
$$ \left\{ \begin{array}{c} x-\arctan y=y-\arctan x \\ x^2-xy+4y^2=4 \end{array} \right. $$
Thank you!!
Without loss of generality we may suppose that $x\ge y$. But if $x>y$, what is the sign of $(\arctan y-\arctan x)$ ? conclude that $x=y$ and finish the job.