  The nonzero and relatively large $\theta_{13}$ have been reported by Daya
Bay, T2K, MINOS, and Double Chooz Collaborations. In order to accommodate the
nonzero $\theta_{13}$, we modified the tribimaximal (TB), bimaxima (BM), and
democratic (DC) neutrino mixing matrices. From three modified neutrino mixing
matrices, two of them (the modified BM and DC mixing matrices) can give nonzero
$\theta_{13}$ which is compatible with the result of the Daya Bay and T2K
experiments. The modified TB neutrino mixing matrix predicts the value of
$\theta_{13}$ greater than the upper bound value of the latest experimental
results. By using the modified neutrino mixing matrices and impose an
additional assumption that neutrino mass matrices have two zeros texture, we
then obtain the neutrino mass in normal hierarchy when
$(M_{\nu})_{22}=(M_{\nu})_{33}=0$ for the neutrino mass matrix from the
modified TB neutrino mixing matrix and $(M_{\nu})_{11}=(M_{\nu})_{13}=0$ for
the neutrino mass matrix from the modified DC neutrino mixing matrix. For these
two patterns of neutrino mass matrices, either the atmospheric mass squared
difference or the solar mass squared difference can be obtained, but not both
of them simultaneously. From four patterns of two zeros texture to be
considered on the obtained neutrino mass matrix from the modified BM neutrino
mixing matrix, none of them can predict correctly neutrino mass spectrum
(normal or inverted hierarchy).
