Circling a parabola!

Geometry Level 4

From the vertex \(O\) of the parabola \(y^2 = 4ax\), two distinct chords are drawn which intersect the parabola at two distinct points \(P\) and \(Q\). Two circles are then drawn with chords \(OP\) and \(OQ\) as their respective diameters. These circles intersect each other at two points, at \(O\) and at another point inside the parabola, \(R\). Let \(\theta_1\) and \(\theta_2\) be the respective gradients of the tangents to the parabola at \(P\) and \(Q\) respectively and \(\varphi\) be the gradient of the line \(OR\). Find the value of \(\cot \theta_1 + \cot \theta_2\) in terms of \(\varphi\).

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