Angle Chasing

Geometry Level 5

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 \(\alpha\).

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