ormal hierarchy and the inverted hierarchy, respectively. Subsequently, the solar neutrino mass-squared difference can be written in terms of $\kappa$ as follows: $$\begin{aligned}
\Delta m_{\rm sol}^2= {\kappa^2}({\tilde D_{\nu_2}^2-\tilde D_{\nu_1}^2}),
 \end{aligned}$$ which we compare with the observed value.

Working in the diagonal basis of the charged-leptons, one finds $U_{\rm
PMNS}=V_\nu$, which is parameterized by three mixing angles, $\theta_{ij}
(i,j=1,2,3; i < j)$, one CP violating Dirac phase, $\delta_{CP}$, and two Majorana phases, $\{\alpha_{2}, \alpha_{3}\}$, as $$U_{\rm PMNS} = 
\begin{pmatrix} c_{12} c_{13} & s_{12} c_{13} & s_{13} e^{-i \delta_{CP}} \\ 
-s_{12} c_{23} - c_{12} s_{23} s_{13} e^{i \delta_{CP}} & c_{12} c_{23} - s_{12} s_{23} s_{13} e^{i \delta_{CP}} & s_{23} c_{13} \\
s_{12} s_{23} - c_{12} c_{23} s_{13} e^{i \delta_{CP}} & -c_{12} s_{23} - s_{12} c_{23} s_{13} e^{i \delta_{CP}} & c_{23} c_{13} 
\end{pmatrix}
\begin{pmatrix} 1 & 0 & 0 \\ 0 & e^{i \frac{\alpha_{2}}{2}} & 0 \\ 0 & 0 & e^{i \frac{\alpha_{3}}{2}} \end{pmatrix},$$ where $c_{ij}$ and $s_{ij}$ stand for $\cos \theta_{ij}$ and $\sin \theta_{ij}$, respectively. Then, the mixing angles are expressed in terms of the components of $U_{\rm PMNS}$ as $$\begin{aligned}
\sin^2\theta_{13}=|(U_{\rm PMNS})_{13}|^2,\quad 
\sin^2\theta_{23}=\frac{|(U_{\rm PMNS})_{23}|^2}{1-|(U_{\rm PMNS})_{13}|^2},\quad 
\sin^2\theta_{12}=\frac{|(U_{\rm PMNS})_{12}|^2}{1-|(U_{\rm PMNS})_{13}|^2}.\end{aligned}$$ 0 Also we compute the Jarlskog invariant, $\delta_{CP}$ derived from PMNS matrix elements $U_{\alpha i}$: $$J_{CP} = \text{Im} [U_{e1} U_{\mu 2} U_{e 2}^* U_{\mu 1}^*] = s_{23} c_{23} s_{12} c_{12} s_{13} c^2_{13} \sin \delta_{CP},$$ and the Majorana phases are also estimated in terms of other invariants $I_1$ and $I_2$: $$I_1 = \text{Im}[U^*_{e1} U_{e2}] = c_{12} s_{12} c_{13}^2 \sin \left( \frac{\alpha_{2}}{2} \right), \
I_2 = \text{Im}[U^*_{e1} U_{e3}] = c_{12} s_{13} c_{13} \sin \left( \frac{\alpha_{3}}{2}  - \delta_{CP} \right).$$ As for