Constant angle surfaces in product spaces

We classify all the surfaces in M²(_c1)×M²(_c2)$M^2\left(c_1\right)\times M^2\left(c_2\right)$ for which the tangent space _TpM²$T_p{M}^2$ makes constant angles with _Tp(M²(_c1)×{_p2})$T_p(M^2\left(c_1\right)\times \left\{p_2\right\})$ (or equivalently with _Tp({_p1}×M²(_c2))$T_p(\left\{p_1\right\}\times M^2\left(c_2\right))$ for every point p=(_p1,_p2)$p=(p_1,p_2)$ of M²$M^2$. Here M²(_c1)$M^2\left(c_1\right)$ and M²(_c2)$M^2\left(c_2\right)$ are 2$2$-dimensional space forms, not both flat. As a corollary we give a classification of all the totally geodesic surfaces in M²(_c1)×M²(_c2)$M^2\left(c_1\right)\times M^2\left(c_2\right)$.