JEE Math Practice Question

Let $$S$$ be the set of all solutions of the equation $$\cos ^{-1}(2 x)-2 \cos ^{-1}\left(\sqrt{1-x^{2}}\right)=\pi, x \in\left[-\frac{1}{2}, \frac{1}{2}\right]$$. Then $$\sum\limits_{x \in S} 2 \sin ^{-1}\left(x^{2}-1\right)$$ is equal to :

1. A.$$\pi-2 \sin ^{-1}\left(\frac{\sqrt{3}}{4}\right)$$
2. B.$$\pi-\sin ^{-1}\left(\frac{\sqrt{3}}{4}\right)$$
3. C.$$\frac{-2 \pi}{3}$$
4. D.None