Question 165
Let $\alpha$ and $\beta$ be the angles of a scalene triangle $A B C$ at the vertices $A$ and $B$, respectively. Let the bisectors of these angles meet the opposite sides of the triangle at $D$ and $E$, respectively. Prove that the acute angle between the lines $D E$ and $A B$ is not greater than $\frac{|\alpha-\beta|}{3}$.