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Geometry Level 5

From point \(T(7-3\sqrt{3},2\sqrt{3}-3)\) tangents are drawn to parabola \(9x^2 + 4y^2 -84x -100y -12xy +508 = 0\) which touches the parabola at points \(P\) & \(Q\). If \(S\) is focus of the parabola then find the measure of \(\angle TSP + \angle TSQ + \angle PTQ\) in radian correct upto three places of decimal.

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