ISL 2013 G3

In a triangle $A B C$, let $D$ and $E$ be the feet of the angle bisectors of angles $A$ and $B$, respectively. A rhombus is inscribed into the quadrilateral $A E D B$ (all vertices of the rhombus lie on different sides of $A E D B$ ). Let $\varphi$ be the non-obtuse angle of the rhombus. Prove that $\varphi \leqslant \max \{\angle B A C, \angle A B C\}$. (Serbia)