# 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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