Disconcerting disc

Find the Moment of Inertia (in S.I. unit) of a uniform semicircular disc of mass \(M\) and radius \(R\) about an axis parallel to its plane and touching it at circumference while making an angle \(\theta\) with its diameter as shown in the figure.

\(\text{Given Data} : ~ M=12~kg \\ R = 5m \\ \theta = \cos ^{ -1 }{ \left( \frac {\pi }{ 4 } \right) } \)

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