  We show that the assumption of type II seesaw mechanism for small neutrino
masses coupled with $b-\tau$ mass unification in a minimal SUSY SO(10) model
leads not only to a natural understanding of large atmospheric mixing angle
($\theta_{23}$) among neutrinos, as recently pointed out, but also to large
solar angle ($\theta_{12}$) and a small $\theta_{13}\equiv U_{e3}$ as required
to fit observations. This is therefore a minimal, completely realistic grand
unified model for all low energy observations that naturally explains the
diverse mixing patterns between the quark and leptons without any additional
inputs such as extra global symmetries. The proposed long baseline neutrino
experiments will provide a crucial test of this model since it predicts
$U_{e3}\simeq 0.16$ for the allowed range of parameters.
