In the context of the type-I seesaw mechanism, when there is an underlying discrete flavor symmetry, such as $\mu-\tau$ symmetry, at work, $\theta_{13}$ in the active neutrino mixing matrix is zero and leptogenesis can not be realized since there are no complex phases in the heavy-light neutrino mixing. In this work, we demonstrate that the existence of dark matter, which violates the flavor symmetry, renders $\theta_{13}$ non-zero via radiative corrections and provides the complex phase(s) needed for leptogenesis. We also briefly comment on possibilities of explaining BICEP2 results based on inflation.