\label{eta2131}$$ represent the relative CP-parities of the neutrinos $\nu_1$ and $\nu_2$, and $\nu_1$ and $\nu_3$, respectively.

One can express [@SPAS94; @BGKP96; @BGGKP99; @BPP1; @Paramm1] the masses $m_2$ and $m_3$ entering into eq. (\[effmass2\]) for in terms of and , measured in the solar and atmospheric neutrino experiments, and $m_1$, while $|U_{\mathrm{e} j}|^2$, $j=1,2,3$, are related to the mixing angle which controls the solar $\nu_e$ transitions $\theta_{\odot}$, and to the lepton mixing parameter $\sin^2\theta$ limited by the data from the CHOOZ and Palo Verde experiments [@CHOOZ; @PaloV]. Within the convention $m_1 < m_2 < m_3$ we are going to use in what follows, one has ${\mbox{$\Delta  m^2_{\mathrm{atm}}$}}\equiv \Delta m^2_{31}$, where $\Delta m^2_{jk} \equiv m_j^2 - m_k^2$, and $m_3 = \sqrt{m_1^2 + {\mbox{$\Delta  m^2_{\mathrm{atm}}$}}}$. For there are two possibilities, ${\mbox{$ \Delta  m^2_{\odot}$}}\equiv \Delta m^2_{21}$ and ${\mbox{$ \Delta  m^2_{\odot}$}}\equiv \Delta m^2_{32}$, corresponding respectively to two different types of neutrino mass spectrum — with normal and with inverted hierarchy. In the first case one has $m_2 = \sqrt{m_1^2 + {\mbox{$ \Delta  m^2_{\odot}$}}}$, $|U_{\mathrm{e} 1}|^2 = \cos^2\theta_{\odot} (1 - |U_{\mathrm{e} 3}|^2)$, $|U_{\mathrm{e} 2}|^2 = \sin^2\theta_{\odot} (1 - |U_{\mathrm{e} 3}|^2)$, and $|U_{\mathrm{e} 3}|^2 \equiv \sin^2\theta$, while in the second $m_2 = \sqrt{m_1^2 + {\mbox{$\Delta  m^2_{\mathrm{atm}}$}}- {\mbox{$ 