Comb + Geo = Tension

Geometry Level 5

Let \(ABC\) be a triangle with \(AB = AC\). The angle bisectors of \(A\) and \(B\) meet the sides \(BC\) and \(AC\) in \(D\) and \(E\), respectively. Let \(K\) be the incenter of the triangle \(ADC\). Suppose that \( \angle BEK= \dfrac{\pi}{4}\). Find sum of all possible values of \( \angle BAC \).

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