Вычислите: \(2\frac{1}{3} : \left(\frac{5}{8}-\frac{8}{3}\right)+2\cdot1\frac{3}{7}\).

\[\frac{5}{8}-\frac{8}{3}=\frac{15}{24}-\frac{64}{24}=-\frac{49}{24}.\]

\[2\frac{1}{3}=\frac{7}{3},\qquad 1\frac{3}{7}=\frac{10}{7}.\]

\[\frac{7}{3}:\left(-\frac{49}{24}\right)=\frac{7}{3}\cdot\left(-\frac{24}{49}\right)=-\frac{8}{7}.\]

\[2\cdot\frac{10}{7}=\frac{20}{7}.\]

\[-\frac{8}{7}+\frac{20}{7}=\frac{12}{7}=1\frac{5}{7}.\]

Ответ: \(\frac{12}{7}\).