MathNet 2021 — Part 09 Question 54

In a right triangle $ABC$ with right angle $C$ on the sides $BC$, $AC$ and $AB$ points $D, E$ and $F$ correspondingly were chosen so that $\angle DAB = \angle CBE$ and $\angle BEC = \angle AEF$. Prove that $DB = DF$.
(Mykhailo Shtandenko)