Adding inverse tangents by the rule

You will write the rule for the sum of two inverse tangents, the rule for the difference, and a function that finds the acute angle between two lines from their slopes. The checker compares your answers with the values from atan.

The idea. $\tan^{-1}x + \tan^{-1}y$ is $\tan^{-1}\dfrac{x + y}{1 - xy}$ when $xy < 1$. When $xy > 1$ you add $\pi$ if $x > 0$ and subtract $\pi$ if $x < 0$. When $xy = 1$ the sum is $\pm\dfrac{\pi}{2}$. The difference is the sum with $y$ replaced by $-y$.

Your tasks.

1. Finish atan_sum(x, y). Use the three cases of the rule. Do not use atan(x) + atan(y).
2. Finish atan_diff(x, y). Call atan_sum with -y.
3. Finish acute_angle(m1, m2). Two lines with slopes m1 and m2 make the angle abs(atan_diff(m1, m2)) or its supplement. Return the one that is at most $\dfrac{\pi}{2}$.