Difference of Arctangents

Theorem
Let $\arctan a - \arctan b \in \openint {-\dfrac \pi 2} {\dfrac \pi 2}$

Then:
 * $\arctan a - \arctan b = \arctan \dfrac {a - b} {1 + a b}$

where $\arctan$ denotes the arctangent.

Also see

 * Sum of Arctangents