Perform the division operation first, according to the order of operations (BODMAS/PEMDAS).

To divide by a fraction, multiply by its reciprocal.

$$\frac{1}{6} \div \frac{1}{3} = \frac{1}{6} \times \frac{3}{1}$$

$$\frac{1 \times 3}{6 \times 1} = \frac{3}{6}$$

Simplify the fraction:

$$\frac{3}{6} = \frac{1}{2}$$

To do this, find a common denominator. The least common multiple of 5 and 2 is 10.
Convert $\frac{2}{5}$ to an equivalent fraction with a denominator of 10:

$$\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}$$

Convert $\frac{1}{2}$ to an equivalent fraction with a denominator of 10:

$$\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$$

$$\frac{4}{10} + \frac{5}{10} = \frac{4+5}{10} = \frac{9}{10}$$

The simplified expression is $\frac{9}{10}$.