Evaluate: \(\cot ^{-1}\left(-\frac{3}{\sqrt{3}}\right)-\sec ^{-1}\left(-\frac{2}{\sqrt{2}}\right)-\operatorname{cosec}^{-1}(-1)-\tan ^{-1}(1)\)

1
\(\frac{\pi}{6}\)
2
\(-\frac{2 \pi}{3}\)
3
0
4
\(\frac{\pi}{3}\)

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