The value of $$\left(2\frac{6}{7}of4\frac{1}{5}\div\frac{2}{3}\right)\times1\frac{1}{9}\div\left(\frac{3}{4}\times2\frac{2}{3}of\frac{1}{2}\div\frac{1}{4}\right)$$ is:

$$\left(2\frac{6}{7}of4\frac{1}{5}\div\frac{2}{3}\right)\times1\frac{1}{9}\div\left(\frac{3}{4}\times2\frac{2}{3}of\frac{1}{2}\div\frac{1}{4}\right)$$
= $$\left(\frac{20}{7}of\frac{21}{5}\div\frac{2}{3}\right)\times\frac{10}{9}\div\left(\frac{3}{4}\times\frac{8}{3}of\frac{1}{2}\div\frac{1}{4}\right)$$
= $$\left(12\div\frac{2}{3}\right)\times\frac{10}{9}\div\left(\frac{3}{4}\times\frac{4}{3}\div\frac{1}{4}\right)$$
= $$18\times\frac{10}{9}\div\left(\frac{3}{4}\times\frac{16}{3}\right)$$
= $$18\times\frac{10}{9}\div4$$
= $$18\times\frac{10}{9}\times \frac{1}{4}$$ = 5