A line passes through the point \(P=(2,3)\) and makes an angle \(\theta\) \((0 \le \theta < \pi)\) with positive direction of \(x\)-axis. If it meets the lines represented by \(x^2-2xy-y^2 = 0\) at points \(Q\) and \(R\), and \(PQ \cdot PR =17\), then find the number of possible values of \(\theta\).

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*This is a part of my set Practice for JEE 2017.*

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