# Approximate formula

There exist such a formula for large x:
$$\arctan(x)\approx \pi/2-1/x+1/3x^3...$$
I can't understand how it is derived. I tried to get it from Taylor series (for x -> infinity) and understood that here is something different. Can someone help me?
Thank you

$$f(x)=\arctan(1/x); f'(x)=-\frac{1}{1+x^2}; f(x)\approx f(0)+f'(0)(x-0)=\pi/2-x$$