If $y=y(x)$ is the solution of the differential equation,
$\sqrt{4-x^{2}} \frac{\mathrm{~d} y}{\mathrm{~d} x}=\left(\left(\sin ^{-1}\left(\frac{x}{2}\right)\right)^{2}-y\right) \sin ^{-1}\left(\frac{x}{2}\right),-2 \leq x \leq 2, y(2)=\frac{\pi^{2}-8}{4}$, then $y^{2}(0)$ is equal to
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