# Gregory Series

## Theorem

For $-\dfrac \pi 4 \le \theta \le \dfrac \pi 4$:

$\theta = \tan \theta - \dfrac 1 3 \tan^3 \theta + \dfrac 1 5 \tan^5 \theta - \ldots$

## Source of Name

This entry was named for James Gregory.

## Historical Note

James Gregory established the result now known as the Gregory Series in $1671$, or perhaps earlier.