reach a sensitivity to values of ${\mbox{$\left|  < \! m  \! > \right| \ $}}\!\! \sim 0.2~$eV. Up to an order of magnitude better sensitivity, i.e., to ${\mbox{$\left|  < \! m  \! > \right| \ $}}\!\! \cong 2.7\times 10^{-2}$ eV, $1.5\times 10^{-2}~$eV, $5.0\times 10^{-2}~$eV, $2.5\times 10^{-2}$ eV and $3.6\times 10^{-2}$ eV is planned to be achieved in the CUORE [@CUORE], GENIUS [@GENIUS], EXO [@EXO], MAJORANA [@Maj] and MOON [@MOON] experiments [^5], respectively.

In what regards the [$\mbox{}^3 {\rm H}$ $\beta$-decay ]{}experiments, the currently existing most stringent upper bounds on the electron (anti-)neutrino mass $m_{\bar{\nu}_e}$ were obtained in the Troitzk [@MoscowH3] and Mainz [@Mainz] experiments and read $m_{\bar{\nu}_e} < 2.2$ eV. The KATRIN [$\mbox{}^3 {\rm H}$ $\beta$-decay ]{}experiment [@KATRIN] is planned to reach a sensitivity to $m_{\bar{\nu}_e} \sim 0.35$ eV.

In the present article we discuss the possibility of establishing the existence of CP-violation in the lepton sector due to the Majorana CP-violating phases by measuring $\!\!$. The fundamental problem of CP-violation in the lepton sector is one of the most challenging future frontiers in the studies of neutrino mixing. It was noticed in [@BGKP96] (see also [@BGGKP99]) that in the case of a [*large mixing angle solution of the solar 