Найдите значение выражения: \(\frac{9}{10}+\frac{4}{9}:(2-1\frac{11}{21})-1\frac{2}{3}\).

Преобразуем смешанные числа: \(1\frac{11}{21}=\frac{32}{21}\), \(1\frac{2}{3}=\frac{5}{3}\).

\[2-\frac{32}{21}=\frac{42}{21}-\frac{32}{21}=\frac{10}{21}.\]

\[\frac{4}{9}:\frac{10}{21}=\frac{4}{9}\cdot\frac{21}{10}=\frac{14}{15}.\]

\[\frac{9}{10}+\frac{14}{15}-\frac{5}{3}=\frac{27}{30}+\frac{28}{30}-\frac{50}{30}=\frac{5}{30}=\frac{1}{6}.\]

Ответ: \(\frac{1}{6}\).