Grand unification of $\mu -\tau$ Symmetry

Near maximal neutrino mixing needed to understand atmospheric neutrino data can be interpreted to be a consequence of an interchange symmetry between the muon and tau neutrinos in the neutrino mass matrix in the flavor basis. This idea can be tested by a measurement of the neutrino mixing parameter ${\theta }_{13}$ and looking for its correlation with ${\theta }_{23}-\pi \mathrm{/}4$. We present a supersymmetric SU(5) grand unified model for quarks and leptons which obeys this exchange symmetry and is a realistic model that can fit all observations. GUT embedding shifts ${\theta }_{13}$ from its zero $\mu -\tau$ symmetric value to a nonzero value keeping it under an upper limit.