A bit too easy but try it!

Geometry Level 3

\(\triangle ABC\) is a triangle, \(E\) and \(G \) are points on \(AB\), while \(F\) and \(H\) are points on \(AC\), such that \(AE=AF=EH=FG=HB=GC=BC\). Then angle \(\angle BAC\) is in the form \(\dfrac{x}{y}\), where \(x\) and \(y\) are coprime positive integers. Find \(x+y\).

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