integration - Evaluating $intlimits_0^{pi/4}log(1+tan x),mathrm dx$

Can someone give me a hint on how to evaluate the closed form of the following integral? According to Wolfram Alpha, this evaluates to $\dfrac{\pi}8\log(2)$.

$$\int\limits_0^{\pi/4}\log(1+\tan x)\,\mathrm dx$$

Thanks.

p.s - Hints are preferred over complete solutions.

Answer

Hint. By the change of variable

$$x=\frac{\pi}4-u, \qquad dx=-du, \qquad 1+ \tan x=? \qquad \log(1+ \tan x)=?$$