Step-by-step Solution:

\(I=\int_{0}^{\pi / 2} \log \tan x d x\) \[\] (i) Using property \(\int_{0}^{a} f(x) d x=\int_{0}^{a} f(a-x) d x\) \[\] \(I=\int_{0}^{\pi / 2} \log \tan \left(\frac{\pi}{2}-x\right) d x\) \[\] \(I=\int_{0}^{\pi / 2} \log \cot x d x\) \[\] Adding (i) & (ii) \[\] \(2 I=0 \Rightarrow I=0\) \[\] Choice (D)\[\]