  The recent results of the Planck experiment put a stringent constraint on the
sum of the light neutrino masses, m1+m2+m3 < 0.23 eV (95 % CL). On the other
hand, two-zero Majorana mass matrix textures predict strong correlations among
the atmospheric angle and the sum of the masses. We use the Planck result to
show that, for the normal hierarchy case, the texture with vanishing (2,2) and
(3,3) elements is ruled out at a high confidence level; in addition, we
emphasize that a future measurement of the octant of the atmospheric mixing
angle (or the one sigma determination of it based on recent fit to neutrino
data) will put severe constraint on the possible structure of the Majorana mass
matrix. The implication of the above mentioned correlations for neutrinoless
double beta-decay are also discussed, for both normal and inverted orderings.
