Evaluate
\arctan(\left(\cot(A)\right)^{3})+\arctan(\frac{\arctan(2A)}{2})+\arctan(\cot(A))
Differentiate w.r.t. A
\frac{4\left(-4\left(A\arctan(2A)\right)^{2}-3\left(\sin(2A)\right)^{2}-\left(\arctan(2A)\right)^{2}-16A^{2}\right)}{\left(4A^{2}+1\right)\left(-3\left(\sin(2A)\right)^{2}+4\right)\left(\left(\arctan(2A)\right)^{2}+4\right)}
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