If 1 + tan \(\theta \) = \(\sqrt 3 \), then \(\sqrt 3 \) cot \(\theta \) - 1 = _________.

1
\(\frac{{\sqrt 3 + 1}}{2}\)
2
\(\frac{{\sqrt 3 - 1}}{2}\)
3
\(\frac{{2\sqrt 3 - 1}}{2}\)
4
\(\frac{{2\sqrt 3 + 1}}{2}\)

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