\( \int_{-\pi / 3}^{0}\left[\cot ^{-1}\left(\frac{2}{2 \cos x-1}\right)+\cot ^{-1}\left(\cos x-\...
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0\( \int_{-\pi / 3}^{0}\left[\cot ^{-1}\left(\frac{2}{2 \cos x-1}\right)+\cot ^{-1}\left(\cos x-\frac{1}{2}\right)\right] d x \) is equal to
(A) \( \frac{\pi^{2}}{6} \)
(B) \( \frac{\pi^{2}}{3} \)
(C) \( \frac{\pi^{2}}{8} \)
(D) \( \frac{3 \pi^{2}}{8} \)
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