Simplify the following expression: (3)/(4) + (12)/(7) / (4)/(7) of (7)/(3)((10)/(7) - (5)/(8)) x (2)/(3)

$$1\frac{5}{7} = \frac{1 \times 7 + 5}{7} = \frac{12}{7}$$ $$2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$$ $$1\frac{3}{7} = \frac{1 \times 7 + 3}{7} = \frac{10}{7}$$

Substitute these into the expression:

$$\frac{\frac{3}{4} + \frac{12}{7} \div \frac{4}{7} \text{ of } \frac{7}{3}}{\left(\frac{10}{7} - \frac{5}{8}\right) \times \frac{2}{3}}$$

First, calculate "of" (multiplication):

$$\frac{4}{7} \text{ of } \frac{7}{3} = \frac{4}{7} \times \frac{7}{3} = \frac{4 \times 7}{7 \times 3} = \frac{28}{21} = \frac{4}{3}$$

Next, perform the division:

$$\frac{12}{7} \div \frac{4}{3} = \frac{12}{7} \times \frac{3}{4} = \frac{36}{28} = \frac{9}{7}$$

Finally, perform the addition:

$$\frac{3}{4} + \frac{9}{7} = \frac{3 \times 7}{4 \times 7} + \frac{9 \times 4}{7 \times 4} = \frac{21}{28} + \frac{36}{28} = \frac{21 + 36}{28} = \frac{57}{28}$$

So, the numerator is $\frac{57}{28}$.

First, perform the subtraction inside the parentheses:

$$\frac{10}{7} - \frac{5}{8}$$

Find a common denominator, which is $7 \times 8 = 56$:

$$\frac{10 \times 8}{7 \times 8} - \frac{5 \times 7}{8 \times 7} = \frac{80}{56} - \frac{35}{56} = \frac{80 - 35}{56} = \frac{45}{56}$$

Next, perform the multiplication:

$$\frac{45}{56} \times \frac{2}{3} = \frac{45 \times 2}{56 \times 3} = \frac{90}{168}$$

Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 6:

$$\frac{90 \div 6}{168 \div 6} = \frac{15}{28}$$

So, the denominator is $\frac{15}{28}$.

$$\frac{\frac{57}{28}}{\frac{15}{28}} = \frac{57}{28} \times \frac{28}{15}$$

Cancel out the common factor of 28:

$$= \frac{57}{15}$$

Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 3:

$$\frac{57 \div 3}{15 \div 3} = \frac{19}{5}$$

The final answer is $\frac{19}{5}$.