\[3\frac{2}{11} \cdot 1\frac{4}{7} - 4\frac{1}{3}\ :1\frac{1}{12} = \frac{35}{11} \cdot \frac{11}{7} - \frac{13}{3}\ :\frac{13}{12} =\]
\[= 5 - \frac{13}{3} \cdot \frac{12}{13} = 5 - 4 = 1.\]