Simplify the following expression:
$$3\frac{1}{5}\text{ of }2\frac{3}{4}÷\frac{11}{3}+\left(2\frac{1}{5}÷1\frac{2}{5}\text{ of }1\frac{3}{7}-2\frac{1}{3}\right)$$

To solve the expression, we convert the mixed fractions into improper fractions and apply the BODMAS rule:
* $3\frac{1}{5}=\frac{16}{5}$
* $2\frac{3}{4}=\frac{11}{4}$
* $2\frac{1}{5}=\frac{11}{5}$
* $1\frac{2}{5}=\frac{7}{5}$
* $1\frac{3}{7}=\frac{10}{7}$
* $2\frac{1}{3}=\frac{7}{3}$

Substituting these values into the expression:

$$\frac{16}{5}\text{ of }\frac{11}{4}÷\frac{11}{3}+\left(\frac{11}{5}÷\frac{7}{5}\text{ of }\frac{10}{7}-\frac{7}{3}\right)$$

First, simplify the terms inside the parentheses by calculating the 'of' operation:

$$\frac{7}{5}\text{ of }\frac{10}{7}=\frac{7}{5}\times \frac{10}{7}=2$$

Now, solve the division and subtraction inside the parentheses:

$$\frac{11}{5}÷2=\frac{11}{10}$$

$$\frac{11}{10}-\frac{7}{3}=\frac{33-70}{30}=-\frac{37}{30}$$

Next, solve the terms outside the parentheses. Start with the 'of' operation:

$$\frac{16}{5}\text{ of }\frac{11}{4}=\frac{16}{5}\times \frac{11}{4}=\frac{44}{5}$$

Perform the division:

$$\frac{44}{5}÷\frac{11}{3}=\frac{44}{5}\times \frac{3}{11}=\frac{12}{5}$$

Finally, combine the outer result with the inner parenthesis result:

$$\frac{12}{5}+\left(-\frac{37}{30}\right)=\frac{12}{5}-\frac{37}{30}$$

$$=\frac{72-37}{30}=\frac{35}{30}=\frac{7}{6}=1\frac{1}{6}$$