Multiple angles in inverse trigonometric functionsMedium

Inverse Trigonometric Equation Set Summation

Let $S = \left\{ {x:{{\cos }^{ - 1}}x = \pi + {{\sin }^{ - 1}}x\, + si{n^{ - 1}}\left( {2x + 1} \right)} \right\}$ . Then $\sum\limits_{x \in S} {{{\left( {2x - 1} \right)}^2}}$ is equal to ______.

Ask about this question