KöMaL 2011 B4359

A regular tetrahedron is intersected with a plane perpendicular to one of its faces in line $e$. The lines of intersection of this plane with the other three faces enclose angles of $\varphi_1$, $\varphi_2$, $\varphi_3$ with $e$. Determine the possible values of he expression $\mathop{\rm tg}\nolimits^{2}\varphi_1 +\mathop{\rm tg}\nolimits^{2}\varphi_2 +\mathop{\rm tg}\nolimits^{2}\varphi_3$.