\(\arcsin \left(-\frac{1}{\sqrt{2}}\right) = -\frac{\pi}{4}\)
\(\arcsin 1 = \frac{\pi}{2}\)
\(\arcsin \frac{\sqrt{3}}{2} = \frac{\pi}{3}\)
\(-\frac{\pi}{4} + \frac{\pi}{2} - \frac{\pi}{3} = \frac{-3\pi + 6\pi - 4\pi}{12} = -\frac{\pi}{12}\)