The value of $\frac{2}{3}\div\frac{3}{10}$ of $\frac{4}{9}-\frac{4}{5}\times1\times\frac{1}{9}\div\frac{8}{15}+\frac{3}{4}\div\frac{1}{2}$ is:

\(\frac{19}{3}\)

$\frac{2}{3}\div\frac{3}{10}$ of $\frac{4}{9}-\frac{4}{5}\times1\times\frac{1}{9}\div\frac{8}{15}+\frac{3}{4}\div\frac{1}{2}$

= \(\frac{2}{3}\) ÷ \(\frac{12}{90}\) - \(\frac{4}{24}\) + \(\frac{3}{2}\) 

= 5 - \(\frac{1}{6}\)  + \(\frac{3}{2}\) 

= \(\frac{30 - 1 + 9}{6}\)

= \(\frac{38}{6}\) = \(\frac{19}{3}\)