2\frac{1}{3} : (\frac{5}{8} - \frac{8}{3}) + 2 \cdot 1\frac{3}{7}

Convert mixed numbers to improper fractions: \(\frac{7}{3} : (\frac{5}{8} - \frac{8}{3}) + \frac{17}{7}\).

Calculate the expression in parentheses: \(\frac{7}{3} : (\frac{15-64}{24}) + \frac{17}{7} = \frac{7}{3} : (-\frac{49}{24}) + \frac{17}{7}\).

Perform division and multiplication: \(\frac{7}{3} \cdot (-\frac{24}{49}) + \frac{17}{7} = -\frac{8}{7} + \frac{17}{7}\).

Add the fractions: \(\frac{-8+17}{7} = \frac{9}{7}\).

The final answer is \(\frac{9}{7}\).