Вычислите tg π/4*ctg 3π/4+tg π/6*ctg 5π/6.

\[\text{tg}\frac{\pi}{4} \cdot ctg\frac{3\pi}{4} + tg\frac{\pi}{6} \cdot ctg\frac{5\pi}{6} =\]

\[= 1 \cdot ( - 1) + \frac{1}{\sqrt{3}} \cdot \left( - \frac{1}{\sqrt{3}} \right) =\]

\[= - 1 - \frac{1}{3} = - 1\frac{1}{3}\]