Let S be the set of all solutions of the equation
\(\cos^{-1}(2x) - 2\cos^{-1} (\sqrt {1 - x^2}) = \pi,x\in \left[-\frac 12, \frac 12\right].\)
Then \(\sum \limits_{x\in S} 2\sin^{-1} (x^2 - 1)\) is equal to
(1) 0
(2) \(\frac{-2\pi}{3}\)
(3) \(\pi - \sin^{-1}\left(\frac{\sqrt 3}4\right)\)
(4) \(\pi - 2\sin^{-1}\left(\frac{\sqrt 3}4\right)\)
