neutrinos $\nu_{1,2,3}$ into the flavor neutrinos $\nu_{e,\mu,\tau}$. Denoting the atmospheric neutrino mixing angle by $\theta_{23}$, the solar neutrino mixing angle by $\theta_{12}$ and the reactor neutrino mixing angle by $\theta_{13}$, the standard parametrization of $U_{PNMS}$ is given by the Particle Data Group (PDG) [@PDG] to be $U_{PDG}=U^{PDG}_\nu K^{PDG}$: $$\begin{aligned}
U_\nu^{PDG}&=&\left( {\begin{array}{*{20}{c}}
{{c_{12}}{c_{13}}}&{{s_{12}}{c_{13}}}&{{s_{13}}{e^{ - i{\delta _{CP}}}}}\\
{ - {{s_{12}{c_{23}}} - {c_{12}}{s_{23}}{s_{13}}{e^{i{\delta _{CP}}}}} }&{{c_{12}}{c_{23}} - {s_{12}}{s_{23}}{s_{13}}{e^{i{\delta _{CP}}}}}&{{s_{23}}{c_{13}}}\\
{{s_{12}}{s_{23}} - {c_{12}}{c_{23}}{s_{13}}{e^{i{\delta _{CP}}}}}&{ - {c_{12}}{{s_{23}} - {s_{12}}{c_{23}}{s_{13}}{e^{i{\delta _{CP}}}}} }&{{c_{23}}{c_{13}}}
\end{array}} \right),
\nonumber\\
{K^{PDG}} &=& \left( {\begin{array}{*{20}{c}}
{{e^{i{\phi _1}/2}}}&0&0\\
0&{{e^{i{\phi _2}/2}}}&0\\
0&0&{{e^{i{\phi _3}/2}}}
\end{array}} \right),
\label{Eq:U_PDG}\end{aligned}$$ for $c_{ij}=\cos\theta_{ij}$, $s_{ij}=\sin\theta_{ij}$ and similarly $t_{ij}=\tan\theta_{ij}$ ($i,j$=1,2,3), where $\phi_{1,2,3}$ stand for the Majorana phases, from which two independent combinations become the CP-violating Majorana phases.

It is interesting to note that the experimentally allowed region of $\delta_{CP}$ includes $\delta_{CP} = 3\pi/2$ indicating maximal CP violation. From the theoretical point of view, $\delta_{CP}$ arises from phases of flavor neutrino masses to be denoted by $M_{ij}$ ($i,j=e,\mu,\tau$). We have been advocating the following useful relation among $\delta_{CP}$ and $M_{ij}$ [@Useful1; @Useful2]: $$\frac{{{M_{\tau \tau }} - {M_{\mu \mu }}}}{2}\sin 2{\theta _{23}} - {M_{\mu \tau }}\cos 2{\theta_{23}} = \tan {\theta_{13}}\left( {{M_{e\mu }}\cos {\theta_{23}} - {M_{e \tau }}\sin {\theta_{23}}} \right){e^{ - i{\delta _{CP}}}},
\label{Eq:M_nu for 