Given that the inverse trigonometric function assumes principal values only. Let \( x, y \) be any two real numbers in \( [-1,1] \) such that \( \cos^{-1}x - \sin^{-1}y = \alpha, \dfrac{-\pi}{2} \le \alpha \le \pi \).
Then, the minimum value of \( x^2 + y^2 + 2xy\) \(\sin \alpha \) is:
