Integrate : $\int \limits_0^{\large\frac{\pi}{4}} $$\log |1+ \tan x| dx$

Question

\[\begin {array} {1 1} (a)\;\frac{\pi}{4} \log 2 \\ (b)\;\frac{\pi}{\theta} \log 6 \\ (c)\;\frac{\pi}{8} \log 2 \\ (d)\;none \end {array}\]