Find The Angle

Geometry Level 4

In acute \(\triangle ABC\) with \(AB<AC,\) the tangent to the circumcircle passing through \(C\) meets line \(AB\) at \(S.\) Let \(P\) be a point in the interior of \(\triangle ABC\) such that \(SC= SP.\) Lines \(BP, AP\) meet the circumcircle at points \(X, Z\) respectively. Suppose that \(\angle PSZ= 60^{\circ}.\) Find \(\angle SZX\) in degrees.

Details and assumptions
- The diagram shown is not accurate, so don't rely on it for non-trivial observations.
- This problem is inspired by IMOSL 2010 G2.


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