A ring of mass `M` and radius `R` lies in `x-y` plane with its centre at origin as shown. The mass distribution of ring is non uniform such that, at any point `P` on the ring, the mass per unit length is given by `lamda = lamda_0 cos^2 theta` (where `lamda_0` is a positive constant). Then the moment of inertia of the ring about z-axis is :
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