Ctg(2п-3 arcsin √ 3/2)

[latex]ctg(3 \alpha )=\frac{ctg^2 \alpha -3ctg \alpha }{3ctg^2 \alpha -1}\\\\ctg(2\pi -3arcsin\frac{\sqrt3}{2})=-ctg(3\cdot \frac{ \pi }{3})=-\frac{ctg^2\frac{\pi }{3}-3ctg\frac{\pi }{3}}{3ctg^2\frac{\pi }{3}-1}=\\\\=-\frac{\frac{1}{3}-3\cdot \frac{\sqrt3}{3} }{3\cdot \frac{1}{3}-1}=-\frac{1-3\sqrt3}{3\cdot (1-1)}\; \to \; \infty [/latex]