Simple Yet Challenging Integral

Calculus Level 3

Evaluate the definite integral $\displaystyle{\int _{ 0 }^{ \frac{\pi}{4}}{ \ln { (\tan { x+1)\, dx } } } .}$ The answer must be a decimal in terms of $\pi$ . For example, if the calculation result is $2.654\pi,$ then the answer should be $2.654$ .