hard geometry problem

[sogood]

Here is a problem connected to geometry. Given triangle $ABC$ where $I$ is the incenter and $O$ is the circumcenter. The inscrbed circle in $ABC$ touches AB,BC and AC respectively in the points $D,E$ and $F$. Let $P$ is a point of the straight line $EF$ such that $DP$ and $EF$ are perpendicular. $PI$ intersects $CO$ in $X$. Prove that the sum of the angles $ACB$ and $AXB$ is $180$.
It's very difficult. I've got one solution but it contains complex numbers. I want to find something easier.
Don't worry to write in russian. I

[Dan B-Yallay]

According to the Rules of this forum you're expected to show at least some attempts to solve the problem.