What is the value of $$ 3\frac{3}{4} - \frac{61}{122} + \frac{9}{2} \div \frac{1}{2}  of  \frac{4}{3} \left(1 + \frac{1}{3}\right) + \frac{1}{2} \times \frac{4}{3}$$?

= $$ 3\frac{3}{4} - \frac{61}{122} + \frac{9}{2} \div \frac{1}{2} of \frac{4}{3} \left(1 + \frac{1}{3}\right) + \frac{1}{2} \times \frac{4}{3}$$

= $$\frac{15}{4}-\frac{1}{2}+\frac{9}{2}\div\frac{2}{3}\times\left(\frac{4}{3}\right)+\frac{2}{3}$$

= $$\frac{15}{4}-\frac{1}{2}+\frac{9}{2}\times\frac{3}{2}\times\frac{4}{3}+\frac{2}{3}$$

= $$\frac{15}{4}-\frac{1}{2}+9+\frac{2}{3}$$

= $$\frac{45}{12}-\frac{6}{12}+\frac{108}{12}+\frac{8}{12}$$

= $$\frac{39}{12}+\frac{108}{12}+\frac{8}{12}$$

= $$\frac{155}{12}$$