Trig-gono-metry-1

Geometry Level 3

In a rectangle \(ABCD\) with sides \(AB=6\) and \(BC=3\), point \(P\) is chosen on \(AB\) such that \(\angle APD = 2\angle CPB\). Then \(AP= a-b\sqrt c\), where \(a\), \(b\) and \(c\) are positive integers with \(c\) being square-free. Find the value of \(a+b+c\).

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