\[1\frac{7}{48} \cdot 2\frac{2}{5} - \left( 9\frac{1}{6} \cdot \frac{4}{15} + 2\frac{5}{9} \right) \cdot \frac{2}{5} =\]
\[= \frac{55 \cdot 12}{48 \cdot 5} - \left( \frac{55 \cdot 4}{6 \cdot 15} + \frac{23}{9} \right) \cdot \frac{2}{5} =\]
\[= \frac{11}{4} - \frac{55 \cdot 4 \cdot 2}{6 \cdot 15 \cdot 5} - \frac{23 \cdot 2}{9 \cdot 5} =\]
\[= \frac{11}{4} - \frac{44}{45} - \frac{46}{45} = \frac{11}{4} - \frac{90}{45} =\]
\[= \frac{11}{4} - 2 = 2\frac{3}{4} - 2 = \frac{3}{4}\]