Вычислите tg165 градусов

[latex]tg165^\circ=tg(180^\circ-15^\circ)=-tg15^\circ=-tg(45^\circ-30^\circ)=\\\\= -\frac{tg45^\circ-tg30^\circ}{1+tg45^\circ\cdot tg30^\circ}=-\frac{1-\frac{\sqrt3}{3}}{1+1\cdot \frac{\sqrt3}{3}} =-\frac{(3-\sqrt3)\cdot 3}{3\cdot (3+\sqrt3)} =-\frac{3-\sqrt3}{3+\sqrt3} =-\frac{(3-\sqrt3)^2}{9-3} =\\\\=-\frac{12-6\sqrt3}{6}=-\frac{6(2-\sqrt3)}{6}=-(2-\sqrt3)=\sqrt3-2 [/latex]