  Recent experiments indicate a departure from the exact Tri-Bimaximal mixing
by measuring definitive non-zero value of $\theta_{13}$. Within the framework
of type I seesaw mechanism, we reconstruct the triangular Dirac neutrino mass
matrix from the $\mu-\tau$ symmetric mass matrix. The deviation from $\mu-\tau$
symmetry is then parametrized by adding dimensionless parameters $y_i$ in the
triangular mass matrix. In this parametrization of the neutrino mass matrix,
the non-zero value $\theta_{13}$ is controlled by $\Delta y = y_4 - y_6$. We
also calculate the resulting leptogenesis and show that the triangular texture
can generate the observed baryon asymmetry in the universe via leptogenesis
scenario.
