4) \(2\arcsin\left(-\frac{\sqrt3}{2}\right)+\arctg(-1)+\arccos\frac{\sqrt2}{2}\)

\(\arcsin(-\sqrt3/2)=-\pi/3\), \(\arctg(-1)=-\pi/4\), \(\arccos(\sqrt2/2)=\pi/4\).

\[2\left(-\frac{\pi}{3}\right)-\frac{\pi}{4}+\frac{\pi}{4}=-\frac{2\pi}{3}.\]

Ответ: \(-\frac{2\pi}{3}\).