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We phenomenologically build a neutrino mass matrix obeying $\mu-\tau$symmetry with only two parameters, Cabibbo angle $(\lambda)$ and a flavourtwister parameter $(\eta)$. For vanishing $\eta$, the model assumes TBM mixing.When $\eta=\lambda$, the model generates a solar mixing angle and solar masssquared difference that coincide with the experimental best-fits. It motivatesus 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 thebreaking of $\mu-\tau$ symmetry, by choosing a proper unitary diagonalizingcharged lepton matrix, and this ensures that $\theta_{23}$ lies within thefirst octant. The Cabibbo angle $(\lambda=\sin\theta_{c})$ plays the role of aguiding parameter in both neutrino as well as leptonic sector. The effect ofthe Dirac CP violating phase $\delta_{cp}$ is also studied when it enterseither through the charged lepton diagonalizing matrix or through neutrinomixing matrix.

Leptonic mixing matrix in terms of Cabibbo angle