\[\left( 30\ :27 - \frac{1}{3} \right) \cdot 2\frac{1}{7} + \frac{2}{5} =\]
\[= \left( \frac{30}{27} - \frac{1}{3} \right) \cdot \frac{15}{7} + \frac{2}{5} =\]
\[= \left( \frac{10}{9} - \frac{1^{\backslash 3}}{3} \right) \cdot \frac{15}{7} + \frac{2}{5} =\]
\[= \frac{7}{9} \cdot \frac{15}{7} + \frac{2}{5} = \frac{5^{\backslash 5}}{3} + \frac{2^{\backslash 3}}{5} =\]
\[= \frac{31}{15} = 2\frac{1}{15}.\]