Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2016 / Paper 1 / 3 / b / Solution

For $u>0$, the principal inverse tangent satisfies $\arctan u+\arctan (1/u)=\pi /2$: the two positive acute angles are complementary. Taking $u=\pi /4$ therefore makes the argument of the natural logarithm equal to $(2/\pi )(\pi /2)=1$. The requested value is $\ln 1=0$.