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

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

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

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