## One small step

Weird fact of the day: $arctan(x)+arctan(x^{-1})=sgn(x)\frac{\pi}{2}, x \neq 0$.

Why is it weird? Because the sum of two clearly non-constant functions is constant. Well, more or less so.

How to prove it? Differentiate.

How can I use it? You can confuse people with it: “Hello, clerk, I want $2arctan(e^{\pi})/\pi+2arctan(e^{-\pi})/\pi$” tickets to this movie.” Also, it works as a very fancy, if slightly incorrect way to write signum function.