$$\begin{aligned} &\left(1\frac{1}{35}:-\frac{4}{5}\right)\cdot3\frac{1}{3}=\\ &\left(\frac{36}{35}:-\frac{4}{5}\right)\cdot\frac{10}{3}=\\ &\left(\frac{36}{35}\cdot\left(-\frac{5}{4}\right)\right)\cdot\frac{10}{3}=\\ &\left(-\frac{9}{7}\right)\cdot\frac{10}{3}=\\ &-\frac{3}{7}\cdot\frac{10}{1}=\\ &=-\frac{30}{7}=\\ &=-4\frac{2}{7} \end{aligned}$$
Ответ: $$-4\frac{2}{7}$$