A ring of mass $M$ and radius $R$ lies in $x-y$ plane with its centre at origin as shown. The mass distribution of rings is non-uniform such that at any point $P$ on the ring, the mass per unit length is given by $\lambda ={\lambda }_0 {\cos }^2\theta$ ( where ${\lambda }_0$ is a positive constant). Then the moment of inertia of the ring about $z$- axis is