This does NOT involve a differential and certainly is NOT a differential equation! There is no "formula" or "trick" to this, just look for values of x so that \(\displaystyle x arctan(x)= 0\). It is simply algebra- solve this equation.

I would start by using "Desmos",

https://www.desmos.com/calculator, to graph \(\displaystyle y= x arctan(x)\) and \(\displaystyle y= \frac{\pi}{2}- 1\). It appears that \(\displaystyle x arctan(x)>\frac{\pi}{2}\) for x< -0.826 and x> 0.826, approximately.