Resolver o sistema

$\{\begin{array}{l}{\mathrm{tg}}^{2}x+{\mathrm{tg}}^{2}y=6\\ \frac{\mathrm{tg}x}{\mathrm{tg}y}+\frac{\mathrm{tg}y}{\mathrm{tg}x}=-6\end{array}$

Sabendo que $x$ e $y$ pertencem ao intervalo $[-\pi /2,\pi /2]$.