Angle Chasing

Let $ABC$ be an acute-angled triangle, and let $D,E,F$ be points on $BC, CA,AB$ respectively such that $AD$ is the median, $B$ E is the internal angle bisector and $CF$ is the altitude. Suppose $\angle FDE= \angle ACB , \angle DEF=\angle BAC$ and $\angle EFD =\angle ABC$ . If $\angle BAC +\angle ABC= \alpha$ , submit your answer as sum of all positive integer divisors of $\alpha$ .