  Realistic neutrino mixing is achieved at one-loop level radiatively using
$S3\times Z_2$ symmetry. The model comprises of two right-handed neutrinos,
maximally mixed to produce the structure of the left-handed Majorana neutrino
mass matrix characterized by $\theta_{13}=0$, $\theta_{23}=\pi/4$ and any value
of $\theta_{12}^0$ particular to the Tribimaximal (TBM), Bimaximal (BM) and
Golden Ratio (GR) or other mixings. A small deviation from this maximal mixing
between the two right-handed neutrinos could generate non-zero $\theta_{13}$,
shifts of the atmospheric mixing angle $\theta_{23}$ from $\pi/4$ and also
could correct the solar mixing angle $\theta_{12}$ by a small amount altogether
in a single step. In this scotogenic mechanism of generating non-zero
$\theta_{13}$ by shifting from maximal mixing in the right-handed neutrino
sector, two $Z_2$ odd inert scalar $SU(2)_L$ doublets were used, the lightest
of which can serve as a dark matter candidate.
