If y=y(x) is the solution of the differential equation, √(4-x^2) (d y)/(d x)=(( sin^-1(x/2))^2-y) sin^-1(x/2),-2 ≤ x ≤ 2, y(2)=(π^2-8)/4, then y^2(0)…

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