  On account of the new neutrino oscillation data signalling a non-zero value
for the smallest mixing angle ($\theta_z$), we present an explicit realization
of the underlying U(1) symmetry characterizing the maximal atmospheric mixing
angle ($\theta_y = \pi / 4$) pattern with two degenerate masses but now with
generic values of $\theta_z$. We study the effects of the form invariance with
respect to U(1), and/or $Z_3$, $Z_2$ subgroups, on the Yukawa couplings and the
mass terms. Later on, we specify $\theta_z$ to its experimental best fit value
($ \sim 8^o$), and impose the symmetry in an entire model which includes
charged leptons, and many Higgs doublets or standard model singlet heavy
scalars, to show that it can make room for the charged lepton mass hierarchies.
In addition, we show for the non-tribimaximal value of $\theta_z \neq 0$ within
type-I seesaw mechanism enhanced with flavor symmetry that neutrino mass
hierarchies can be generated. Furthermore, lepton/baryogenesis can be
interpreted via type-II seesaw mechanism within a setup meeting the flavor
U(1)-symmetry.
