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The value of $2 \sin ^{-1}\left(\frac{1}{2}\right)+\cot ^{-1}\left(\frac{1}{\sqrt{3}}\right)$ is
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$\frac{2 \pi}{3}$
$2 \sin ^{-1}\left(\frac{1}{2}\right)+\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)=2 \times \frac{\pi}{6}+\frac{\pi}{3}=\frac{2 \pi}{3}$
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