🚀 go-pugleaf

An expansion of arctan(x) that converges fairly quickly is :

x - x^3/3 + x^5/5 - x^7/7 + x^9/9 - x^11/11 + ...

+ (-1)^k * x^(2n+1) / (2n+1) + ...

There is the condition, however, that -1 < x < 1. Actually, it also
works for x = +1 or -1. If your slope is between 1 and +oo, or
-1 and -oo, just take x=1/m and remember that your angle is now
between your line and the vertical, not the horizontal.

To get the expansion, you just integrate the power series expansion
of 1 / (1 + x^2).

1 / (1 + x^2) is just 1 / [1 - (-x^2)]

or 1 - x^2 + x^4 - x^6 + ... provided that -1 < -x^2 < 1.

Brian.