\begin{aligned}
&1+\frac{2}{3}-3 \div\left(1+\frac{2}{3} \text { of } \frac{6}{7}\right) \\
&=\frac{5}{3}-3 \div\left(1+\frac{2}{3} \times \frac{6}{7}\right) \\
&\frac{5}{3}-3 \div\left(1+\frac{4}{7}\right) \\
&=\frac{5}{3}-3 \div\left(\frac{11}{7}\right) \\
&=\frac{5}{3}-3 \times \frac{7}{11}=\frac{5}{3}-\frac{21}{11} \\
&=-\frac{8}{33}
\end{aligned}