Sum of two reciprocals

Geometry Level 4

Let ABC be an isosceles triangle where \(AB=AC=1\). D and E are the midpoints of AB and AC respectively. Two lines are projected from points B and C and meet an extended DE at arbitrary points F and G respectively such that \(BC=FG\). If they cut AC and AB at points P and Q respectively, \(\frac{1}{BQ} + \frac{1}{CP}\) = \(?\)

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