ABC problem?

Geometry Level 4

In \(\triangle ABC\), we have \(AB \times AC=BC^2-AB^2\). If \(\angle ABC=\theta\) radians, it follows that \(\angle BCA=\dfrac{p\pi-q\theta}{r} \) radians, where \(p\), \(q\) and \(r\) are positive integers. What is the minimum possible value of \(p+q+r\)?

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