Recently, the reactor mixing angle $theta_{13}$ has been measured precisely by Daya Bay, RENO and T2K experiments with a moderately large value. However, the standard form of neutrino mixing patterns such as bimaximal, tri-bimaximal, golden ratio of
types A and B, hexagonal etc., which are based on certain flavor symmetries, predict vanishing $theta_{13}$. Using the fact that the neutrino mixing matrix can be represented as $V_{rm PMNS}=U_l^{dagger} U_ u P_ u$, where $U_l$ and $U_ u$ result from the diagonalization of the charged lepton and neutrino mass matrices and $P_ u$ is a diagonal matrix containing Majorana phases, we explore the possibility of accounting for the large reactor mixing angle by considering deviations both in the charged lepton and neutrino sector. In the charged lepton sector we consider the deviation as an additional rotation in the (12) and (13) planes, whereas in neutrino sector we consider deviations to various neutrino mixing patterns through (13) and (23) rotations. We find that with the inclusion of these deviations it is possible to accommodate the observed large reactor mixing angle $theta_{13}$, and one can also obtain limits on the CP violating Dirac phase $delta_{CP}$ and Jarlskog invariant $J_{CP}$ for most of the cases. We then explore whether our findings can be tested in the currently running NO$ u$A experiment with 3 years of data taking in neutrino mode followed by 3 years with anti-neutrino mode.
