for seesaw}\\
{m_3}{e^{ - i{\phi _3}}} &=& \frac{{c_{13}^2\left( {a_ + ^2 + b_ + ^2} \right) - s_{13}^2\left( {a_1^2 + b_1^2} \right)}{e^{ - 2i{\delta _{CP}}}}}{{\cos 2{\theta _{13}}}}.
\nonumber\end{aligned}$$ These three relations Eqs.(\[Eq:23 for seesaw\]), (\[Eq:12 for seesaw\]) and (\[Eq:13 for seesaw\]) can be casted into more compact forms since one of three neutrino masses turns out be zero owing to $\det(M_\nu)=0$. For NH, we have $m_1=0$ leading to $$a_ - ^2 + b_ - ^2 = \frac{1}{{{t_{12}}{c_{13}}}}\left( {{a_1}{a_ - } + {b_1}{b_ - }} \right),
\label{Eq:m1=0 for seesaw}$$ and obtain that $$\begin{aligned}
&&
{a_ + }{a_ - } + {b_ + }{b_ - } =  - {t_{13}}\left( {{a_1}{a_ - } + {b_1}{b_ - }} \right){e^{ - i{\delta _{CP}}}},
\label{Eq:23 for NHseesaw}\\
&&
a_1^2 + b_1^2 - t_{12}^2\left( {a_ - ^2 + b_ - ^2} \right) = {t_{13}}\left( {{a_1}{a_ + } + {b_1}{b_ + }} \right){e^{i{\delta _{CP}}}},
\label{Eq:12 for NHseesaw}\\
&&
c_{13}^2\left( {a_1^2 + b_1^2} \right) - s_{13}^2\left( {a_ + ^2 + b_ + ^2} \right){e^{2i{\delta _{CP}}}} = \left( {c_{13}^2 - s_{13}^2} \right)t_{12}^2\left( {a_ - ^2 + b_ - ^2} \right),
\label{Eq:13 for NHseesaw}\end{aligned}$$ and $$\begin{aligned}
{m_2}{e^{ - i{\phi _2}}} &=& \frac{1}{{c_{12}^2}}\left( {a_ - ^2 + b_ - ^2} \right),
\nonumber\\
