2013 IMO Shortlist 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 $\varphi \leq \max \{\angle B A C, \angle A B C\}$. (Serbia)

在三角形$A B C$中，令$D$和$E$分别为角$A$和$B$的角平分线的脚。四边形 $A E D B$ 内接一个菱形(菱形的所有顶点都位于 $A E D B$ 的不同边上)。令 $\varphi$ 为菱形的非钝角。证明 $\varphi \leq \max \{\angle B A C, \angle A B C\}$。 (塞尔维亚)