\[2\frac{3}{4} \cdot \frac{2}{3}\ :3\frac{2}{3} = \frac{11}{4} \cdot \frac{2}{3}\ :\frac{11}{3} =\]
\[= \frac{11}{6} \cdot \frac{3}{11} = \frac{1}{2}.\]