<s>[INST] Prove that $ \frac{1}{2}\cot^{-1}\frac{2\sqrt[3]{4}+1}{\sqrt{3}}+\frac{1}{3}\tan^{-1}\frac{\sqrt[3]{4}+1}{\sqrt{3}}=\dfrac{\pi}{6}. $ Prove that $$ \frac{1}{2}\cot^{-1}\frac{2\sqrt[3]{4}+1}{\sqrt{3}}+\frac{1}{3}\tan^{-1}\frac{\sqrt[3]{4}+1}{\sqrt{3}}=\dfrac{\pi}{6}. $$
 [/INST] Use the following identities:
$$\arctan a \pm\arctan b=\arctan\left(\frac{a\pm b}{1\mp ab}\right)$$
$$\arctan a+\mathrm{arccot} \hspace{2pt}a=\frac{\pi}{2},\hspace{10 pt}\forall a>0$$
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