\(\int\limits_0^{\frac{\pi }{2}} {\log (\tan x)dx}\) is equal to

1
\(- \frac{\pi }{2}{\log _e}2\)
2
\(- \pi {\log _e}2\)
3
\(\frac{\pi }{2}{\log _e}2\)
4
None of these

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