Ответ:

\[1\frac{2}{3}+2\frac{1}{6}=\frac{5}{3}+\frac{13}{6}=\frac{10}{6}+\frac{13}{6}=\frac{23}{6}\]

\[\frac{23}{6}\div\frac{3}{4}=\frac{23}{6}\times\frac{4}{3}=\frac{46}{9}=5\frac{1}{9}\]

Ответ: \(5\frac{1}{9}\).