Pattern of the Approximate Mass Degeneracy of Majorana Neutrinos

In view of the recently reported evidence for a nonzero Majorana mass of the electron neutrino, together with the established phenomena of atmospheric and solar neutrino oscillations, the case of three nearly mass-degenerate Majorana neutrinos is now a distinct possibility. I show in this paper how a natural pattern of symmetry breaking in the recently proposed $A_4$ model of Majorana neutrino masses can accommodate the data on neutrino oscillations, resulting in the predictions $\sin^2 2 \theta_{atm} = 1$ and $\sin^2 2 \theta_{sol} = 2/3$.