Answer
$$ = -{{2\,\left(2\,\arctan \left({{2\,\sin x+\cos x+1}\over{\sqrt{3}\, \left(\cos x+1\right)}}\right)-\sqrt{3}\,\arctan \left({{\sin x }\over{\cos x+1}}\right)\right)}\over{\sqrt{3}}} $$
Explanation
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