Integrate[Sqrt[D[Sin[t]/(Sin[t/2] + Cos[t/2]), t]^2 + D[-Cos[t]/(Sin[t/2] + Cos[t/2]), t]^2 + D[Sqrt[3] - Sqrt[3]/(Sin[t/2] + Cos[t/2]), t]^2], t,0,pi]

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