Question

3/43 П (5arcctg(-1)+arcsin1/2+arctg(-корень из 3) )

Answer 1

$\frac{3}{43}\cdot \pi \cdot (5\, arcctg(-1)+arcsin\frac{1}{2}+arctg(-\sqrt3))=\\\\= \frac{3\pi }{43}\cdot (5\cdot (-\frac{\pi}{4})+\frac{\pi}{6}-\frac{\pi }{3} )=\frac{3\pi }{43}\cdot \frac{-15\pi +2\pi -4\pi }{12}=\frac{\pi }{43}\cdot \frac{-17\pi }{4}=-\frac{17\pi ^2}{172}$