Leptonic mixing matrix in terms of Cabibbo angle

We phenomenologically build a neutrino mass matrix obeying $\mu-\tau$ symmetry with only two parameters, Cabibbo angle $(\lambda)$ and a flavour twister parameter $(\eta)$. For vanishing $\eta$, the model assumes TBM mixing. When $\eta=\lambda$, the model generates a solar mixing angle and solar mass squared difference that coincide with the experimental best-fits. It motivates us to propose a mixing matrix in the neutrino sector with $ sin\theta_{12}<\frac{1}{\sqrt{3}}$, $\theta_{13}=0$ and $\theta_{23}=\pi/4$. The corrections in $\theta_{13}$ and $\theta_{23}$ are conducted following the breaking of $\mu-\tau$ symmetry, by choosing a proper unitary diagonalizing charged lepton matrix, and this ensures that $\theta_{23}$ lies within the first octant. The Cabibbo angle $(\lambda=\sin\theta_{c})$ plays the role of a guiding parameter in both neutrino as well as leptonic sector. The effect of the Dirac CP violating phase $\delta_{cp}$ is also studied when it enters either through the charged lepton diagonalizing matrix or through neutrino mixing matrix.