If $\cos^{-1}x-\cos^{-1}\left(\dfrac{y}{2}\right)=\alpha$, where $-1\le x\le1,\ -2\le y\le2,\ x\le\dfrac{y}{2}$, then for all $x,y$, the value of $4x^{2}-4xy\cos\alpha+y^{2}$ is: