ArcTan[(2 z Sqrt[1 - z^2])/(1 - 2 z^2)] == -2 ArcCos[z] - (Pi/2) (Sqrt[1/z] Sqrt[z] Sqrt[1/(-1 + Sqrt[2] z)] Sqrt[-1 + Sqrt[2] z] - Sqrt[-(1/z)] Sqrt[-z] Sqrt[-1 - Sqrt[2] z] Sqrt[-(1/(1 + Sqrt[2] z))] + Sqrt[z^2]/z + (z Sqrt[-1 + z^2])/ Sqrt[-z^2 + z^4] - 2)

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2003-08-21