4 cos(-8п/3)*ctg(-3п/4)*sin(3п/2)

[latex]4 cos(-\frac{8\pi}{3})ctg(-\frac{3\pi}{4})sin(\frac{3\pi}{2})\\ -4cos(\frac{8\pi}{3})ctg(\frac{3\pi}{4})sin(\frac{3\pi}{2})=\\-4cos(2\pi+(\pi-\frac{\pi}{3}))ctg(\pi-\frac{\pi}{4})sin(\pi+\frac{\pi}{2})=\\4cos\frac{\pi}{3}ctg\frac{\pi}{4}sin\frac{\pi}{2}=4*\frac{1}{2}*1*1=2.[/latex]