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