A functional equation problem calculus

Question

If $f(x)+f(1-1/x)=\arctan(x)$, find $f(x)+f(1-x)$.

Answer 1

I found this path, maybe there is shorter:

• Set $g(x)=f(x)+f(1-\frac 1x)=\arctan(x)$
• Calculate $g(\frac 1x)$ and $g(1-x)$
• Show $2f(1-x)=\arctan(1-x)-\arctan(\frac{x}{x-1})+\arctan(\frac 1x)$
• Deduce $2f(x)$
• Calculate $f(x)+f(1-x)$ using $\arctan(a)+\arctan(\frac 1a)=\frac \pi 2$