hello
I need help solving this:

arccot x =(pi/2)-x+(x^3/3)-(x^5/5)+...

I need to know how many terms are needed in this series to compute arccotx for x^2<1 accurate to 12 decimal places rounded

I know i should solve Error<(1/2)*10^-12

but i have no idea of the error

thank you everyone