Focusing on Incenters #2

Geometry Level 4

Suppose that \(\triangle ABC\) has incenter \(I\) and that \(BI, \ CI\) meet \(AC, \ AB\) at \(D, \ E\) respectively. Suppose further that the bisector of \(\angle BIC\) meets \(BC, \ DE\) at \(P, \ Q\) respectively, and that \(PI = 2QI\). Find the value of \(\angle BAC\) in degrees.

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