The value of $$\frac{2}{3} \div \frac{3}{{10}}{\text{ of }}\frac{4}{9} - \frac{4}{5} \times 1\frac{1}{9} \div \frac{8}{{15}} + \frac{3}{4} \div \frac{1}{2}{\text{ is:}}$$

$$\eqalign{ & \frac{2}{3} \div \frac{3}{{10}}{\text{ of }}\frac{4}{9} - \frac{4}{5} \times 1\frac{1}{9} \div \frac{8}{{15}} + \frac{3}{4} \div \frac{1}{2} \cr & = \frac{2}{3} \div \frac{2}{{15}} - \frac{4}{5} \times \frac{{10}}{9} \times \frac{{15}}{8} + \frac{3}{4} \times 2 \cr & = \frac{2}{3} \times \frac{{15}}{2} - \frac{5}{3} + \frac{3}{2} \cr & = 5 - \frac{5}{3} + \frac{3}{2} \cr & = \frac{{29}}{6} \cr} $$