б) \(2\frac{3}{4}:\left(1\frac{1}{2}-\frac{2}{5}\right)+\left(\frac{3}{4}+\frac{5}{6}\right):3\frac{1}{6};\)

б) Выполним действия:

1) $$1\frac{1}{2} - \frac{2}{5} = \frac{3}{2} - \frac{2}{5} = \frac{3 \cdot 5 - 2 \cdot 2}{10} = \frac{15 - 4}{10} = \frac{11}{10};$$

2) $$2\frac{3}{4} : \frac{11}{10} = \frac{11}{4} : \frac{11}{10} = \frac{11}{4} \cdot \frac{10}{11} = \frac{11 \cdot 10}{4 \cdot 11} = \frac{10}{4} = \frac{5}{2};$$

3) $$ \frac{3}{4} + \frac{5}{6} = \frac{3 \cdot 3 + 5 \cdot 2}{12} = \frac{9 + 10}{12} = \frac{19}{12};$$

4) $$ \frac{19}{12} : 3\frac{1}{6} = \frac{19}{12} : \frac{19}{6} = \frac{19}{12} \cdot \frac{6}{19} = \frac{19 \cdot 6}{12 \cdot 19} = \frac{6}{12} = \frac{1}{2};$$

5) $$ \frac{5}{2} + \frac{1}{2} = \frac{6}{2} = 3.$$

Ответ: 3.