Integrate[(1 - Cos[2 p] (2 - Cos[p]))/ Sqrt[(2 - Cos[p])^2 - 1], {p, 0, 2 \[Pi]}]Integrate[(1 - Cos[2 p] (2 - Cos[p]))/ Sqrt[(2 - Cos[p])^2 - 1], {p, 0, 2 \[Pi]}]

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