We suggest that the weak-basis independent condition det(M_nu)=0 for the
effective neutrino mass matrix can be used in order to remove the ambiguities
in the reconstruction of the neutrino mass matrix from input data available
from present and future feasible experiments. In this framework, we study the
full reconstruction of M_nu with special emphasis on the correlation between
the Majorana CP-violating phase and the various mixing angles. The impact of
the recent KamLAND results on the effective neutrino mass parameter is also
briefly discussed.Comment: 11 pages, 4 figures. Comments and references added; final version to
appear in Phys. Lett.