\[(E): ({ z }^{ 2 }-2z)\cos ^{ 2 }{ \alpha +1=0 }\]

The equation \((E)\) admits 2 solutions \( U\) and \(V\). If \(U\times V=\cos ^{ n } \alpha \), find \(n\).

**Bonus**: Find the set of images of these solutions.

**Clarification**: \(z\) is a complex number.

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