Evaluate: (3/4 + 1 5/7) / (4/7 of 2 1/3) / ((1 3/7 - 5/8) * 2/3)

The numerator is $\frac{3}{4} + \frac{12}{7} \div \frac{4}{7} \text{ of } \frac{7}{3}$.
First, calculate the "of" part:

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

Now the numerator becomes:

$$\frac{3}{4} + \frac{12}{7} \div \frac{4}{3}$$

Next, perform the division:

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

Now the numerator becomes:

$$\frac{3}{4} + \frac{9}{7}$$

Perform the addition by finding a common denominator (28):

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

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

The denominator is $\left(\frac{10}{7} - \frac{5}{8}\right) \times \frac{8}{3}$.
First, calculate the expression inside the brackets by finding a common denominator (56):

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

Now the denominator becomes:

$$\frac{45}{56} \times \frac{8}{3}$$

Perform the multiplication:

$$\frac{45}{56} \times \frac{8}{3} = \frac{45 \times 8}{56 \times 3} = \frac{(15 \times 3) \times 8}{(7 \times 8) \times 3} = \frac{15}{7}$$

So, the denominator is $\frac{15}{7}$.

$$\frac{\frac{57}{28}}{\frac{15}{7}} = \frac{57}{28} \div \frac{15}{7}$$

To divide by a fraction, multiply by its reciprocal:

$$\frac{57}{28} \times \frac{7}{15}$$

Simplify before multiplying:

$$\frac{57}{4 \times 7} \times \frac{7}{15} = \frac{57}{4 \times 15}$$

Both 57 and 15 are divisible by 3: $57 \div 3 = 19$ and $15 \div 3 = 5$.

$$\frac{19}{4 \times 5} = \frac{19}{20}$$

The final answer is $\frac{19}{20}$.