If y = y(x) is the solution of the differential equation,  $\sqrt{4-x^2}\frac{dy}{dx}=\left({\left({\sin }^{-1}\left(\frac{x}{2}\right)\right)}^2-y\right){\sin }^{-1}\left(\frac{x}{2}\right)$ $-2\le x\le 2,y\left(2\right)=\left(\frac{{\pi }^2-8}{4}\right)$ ,then y²(0) is equal to ____.