TITLE: How to evaluate $\int_{0}^{\pi}\ln (\tan x)\,dx$
QUESTION [5 upvotes]: How can I integrate $$\int_{0}^{\large\pi}\ln (\tan x)\,\text{dx}\;\;\;?$$

REPLY [6 votes]: If looking for the real value only, it's enough to consider 
$$I=\int_{0}^{\pi/2}\ln (\tan x)dx$$
and let $x=\pi/2-y$
$$I=\int_{0}^{\pi/2}\ln (\tan x)dx=\int_{0}^{\pi/2}\ln (\cot x)dx$$
$$2I=\int_{0}^{\pi/2}\ln (1)dx$$
$$I=0$$