for $a_{1,+,-}$ and $b_{1,+,-}$ and choose several plausible sets of the solutions, which are consistent with the hierarchical condition of $m^2_3\gg m^2_2$ requiring that $\left| a_ + ^2 + b_ + ^2 \right|^2\gg\left| a_ - ^2 + b_ - ^2 \right|^2$ for NH or $m^2_1\approx m^2_2$ requiring that $\left|a_ - ^2 + b_ - ^2 \right|^2\gg\left|{{a_1}{a_ - } + {b_1}{b_ - }} \right|^2$ for IH. As stated in the Introduction, we choose one combination of Dirac neutrino masses to vanish, which includes texture one zero. The discussions on our choices of the solutions are presented in Appendix \[sec:Appendix\], from which we can summarize our results as follows: For NH,

1.  in the case of $a_1 = 0$, $a_{+,-}$ and $b_{1,+,-}$ should satisfy ${a_ - } =  - {{{s_{13}}}}{a_ + }{e^{i{\delta _{CP}}}}/{{{t_{12}}}}$ and ${b_1} = {{{t_{12}}}}{b_ - }/{{{c_{13}}}} + {t_{13}}{b_ + }{e^{i{\delta _{CP}}}}$ as well as ${a_ + }{a_ - } =  - \left( {{b_ + } + {t_{13}}{b_1}e^{ - i{\delta _{CP}}}} \right){b_ - }$ and $a_ - ^2 + b_ - ^2 = {b_1}{b_ - }/{{{t_{12}}{c_{13}}}}$;

2.  in the case of $b_1 = 0$, $a_{1,+,-}$ and $b_{+,-}$ should satisfy relations in the case of $a_1 = 0$ with the interchange 