$\sin {\theta }_{13}$ and neutrino mass matrix with an approximate flavor symmetry

For a neutrino mass matrix whose texture has an approximate flavor symmetry and where one has near degenerate neutrino mass, it is shown that the tribimaximal values for atmospheric angle ${\sin }^2{\theta }_{23}=1\mathrm{/}2$ and solar angle ${\sin }^2{\theta }_{12}=1\mathrm{/}3$ can be maintained even when the reactor angle ${\theta }_{13}\mathrm{\ne }0$. The non zero $\sin {\theta }_{13}$ implies approximate ${\nu }_{\mu }\to -{\nu }_{\tau }$ symmetry instead of ${\nu }_{\mu }\to {\nu }_{\tau }$ symmetry.