Let's calculate the expression:
\[ (2 \frac{3}{4} + 5 \frac{1}{3}) - (3 \frac{1}{3} + 2 \frac{2}{3}) \]
First, add the numbers inside each parenthesis:
\[ (2 \frac{3}{4} + 5 \frac{1}{3}) = 8 \frac{11}{12} \]
\[ (3 \frac{1}{3} + 2 \frac{2}{3}) = 5 \frac{1}{2} \]
Now, subtract the second sum from the first:
\[ 8 \frac{11}{12} - 5 \frac{1}{2} \]
To subtract, find a common denominator, which is 12 in this case:
\[ \frac{99}{12} - \frac{66}{12} \]
Now, subtract the numerators:
\[ \frac{33}{12} \]
Simplify the fraction:
\[ 2 \frac{9}{12} \]
Reduce the fraction:
\[ 2 \frac{3}{4} \]
So, the answer is \( 2 \frac{3}{4} \).