\[1\frac{1}{22} \cdot 3\frac{2}{3} - \left( 2\frac{5}{6} + 3\frac{5}{6} \cdot \frac{7}{23} \right) \cdot \frac{3}{5} =\]
\[= \frac{23 \cdot 11}{22 \cdot 3} - \left( 2\frac{5}{6} + \frac{23 \cdot 7}{6 \cdot 23} \right) \cdot \frac{3}{5} =\]
\[= \frac{23}{6} - \left( 2\frac{5}{6} + \frac{7}{6} \right) \cdot \frac{3}{5} =\]
\[= \frac{23}{6} - 2\frac{12}{6} \cdot \frac{3}{5} =\]
\[= \frac{23^{\backslash 5}}{6} - \frac{4 \cdot 3^{\backslash 6}}{5} =\]
\[= \frac{115}{30} - \frac{12 \cdot 6}{30} =\]
\[= \frac{115 - 72}{30} = \frac{43}{30} = 1\frac{13}{30}\]