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