  Among neutrino mixings, the reactor mixing angle, \theta_{13}, is observed to
be almost vanishing and is consistent with \theta_{13}=0. We discuss how the
condition of \theta_{13}=0 constrains models of neutrino mixings and show that,
for flavor neutrino masses given by M_{ij} (i,j=e,\mu,\tau), two conditions of
M_{e\tau}=-e^{2i\gamma}tan(\theta_{23})M_{e\mu} and
M_{\tau\tau}=e^{4i\gamma}M_{\mu\mu}+e^{2i\gamma}[2/tan(2\theta_{23})]M_{\mu\tau}
lead to \theta_{13}=0, where \theta_{23} is the atmospheric neutrino mixing
angle and \gamma is its associated phase. The rephasing invariance can select
two phases provided by \alpha=arg(M_{e\mu}) and \beta=arg(M_{e\tau}), giving
\gamma=(\beta-\alpha)/2.
