Let's solve the given expression step-by-step:

Step 1: Simplify the division inside the bracket:

\(\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}\)

Step 2: Simplify the addition inside the bracket:

\(\frac{1}{4} + \frac{3}{5} - \frac{1}{3} = \frac{15}{60} + \frac{36}{60} - \frac{20}{60} = \frac{31}{60}\)

Step 3: Now, we have the expression:

\(\frac{\frac{5}{6}}{\frac{31}{60}}\)

Step 4: To divide fractions, we multiply by the reciprocal of the divisor:

\(\frac{5}{6} \times \frac{60}{31} = \frac{300}{186} = \frac{50}{31}\)