Cobimaximal Neutrino Mixing from $A_4$ and its Possible Deviation

It has recently been shown that the phenomenologically successful pattern of cobimaximal neutrino mixing ($\theta_{13} \neq 0$, $\theta_{23} = \pi/4$, and $\delta_{CP} = \pm \pi/2$) may be achieved in the context of the non-Abelian discrete symmetry $A_4$, if the neutrino mass matrix is diagonalized by an orthogonal matrix ${\cal O}$. We study how this pattern would deviate if ${\cal O}$ is replaced by an unitary matrix.