Вычислить: \(-\frac{7}{9} : \left(-\frac{14}{15}\right)^3 - 1\frac{2}{3}\).

\[\left(-\frac{14}{15}\right)^3=-\frac{2744}{3375}.\]

\[-\frac{7}{9}:\left(-\frac{2744}{3375}\right)=\frac{7}{9}\cdot\frac{3375}{2744}=\frac{125}{56}.\]

\[\frac{125}{56}-1\frac{2}{3}=\frac{125}{56}-\frac{5}{3}=\frac{375-280}{168}=\frac{95}{168}.\]

Ответ: \(\frac{95}{168}\).