Sum the products

Algebra Level 5

Let \( \displaystyle P(n)=\prod_{k=0}^{n} (\sin(k^\circ)+\cos(k^\circ))\) and \( \displaystyle F(x)=\sum_{j=0}^{180} P(j) \cdot x^{j} \). Find the degree of the polynomial \(F(x)\).

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