Arcсtg(-√3/3)-arcsin 0+arcсos(-1/2)=

[latex]arcctg(- \frac{ \sqrt{3} }{3})- arcsin0+arccos(- \frac{1}{2}) =( \pi - arcctg( \frac{ \sqrt{3} }{3})-\\- 0 + ( \pi - arccos( \frac{1}{2}) = ( \pi - \frac{ \pi }{3}) + ( \pi - \frac{ \pi }{3} )= 2 \pi - \frac{2 \pi }{3} =\\= \frac{6\pi-2\pi}{3} = \frac{4\pi}{3} [/latex]