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After the successful determination of the reactor neutrino mixing angle\theta_13 ~ 0.16 \neq 0, a new feature suggested by the current neutrinooscillation data is a sizeable deviation of the atmospheric neutrino mixingangle \theta_23 from \pi/4. Using the fact that the neutrino mixing matrix U =U_e^\dagger U_\nu, where U_e and U_\nu result from the diagonalisation of thecharged lepton and neutrino mass matrices, and assuming that U_\nu has a i)bimaximal (BM), ii) tri-bimaximal (TBM) form, or else iii) corresponds to theconservation of the lepton charge L' = L_e - L_\mu - L_\tau (LC), weinvestigate quantitatively what are the minimal forms of U_e, in terms ofangles and phases it contains, that can provide the requisite corrections toU_\nu so that \theta_13, \theta_23 and the solar neutrino mixing angle\theta_12 have values compatible with the current data. Two possible orderingsof the 12 and the 23 rotations in U_e, "standard" and "inverse", areconsidered. The results we obtain depend strongly on the type of ordering. Inthe case of "standard" ordering, in particular, the Dirac CP violation phase\delta, present in U, is predicted to have a value in a narrow interval aroundi) \delta ~ \pi in the BM (or LC) case, ii) \delta ~ 3\pi/2 or \pi/2 in the TBMcase, the CP conserving values \delta = 0, \pi, 2\pi being excluded in the TBMcase at more than 4\sigma. In the addendum we discuss the implications of thelatest 2013 data.

Nonzero |U_e3| from Charged Lepton Corrections and the Atmospheric Neutrino Mixing Angle