Given (\(\frac{3}{4} \div 2\frac{1}{4}\)) of 1 \(\frac{7}{11}\) (3 \(\frac{2}{3}\) - \(\frac{15}{6}\))

1. Simplify the division in the first parentheses: \(\frac{3}{4} \div 2 \frac{1}{4} = \frac{3}{4} \div \frac{9}{4} = \frac{3}{4} \times \frac{4}{9} = \frac{3}{9} = \frac{1}{3}\).

2. Convert the mixed number: \(1 \frac{7}{11} = \frac{18}{11}\).

3. Simplify the subtraction in the second parentheses: \(3 \frac{2}{3} - \frac{15}{6} = \frac{11}{3} - \frac{5}{2} = \frac{22}{6} - \frac{15}{6} = \frac{7}{6}\).

4. The "of" indicates multiplication, so multiply the results: \(\frac{1}{3} \times \frac{18}{11} \times \frac{7}{6} = \frac{126}{198} = \frac{7}{11}\).