Arctangent of Zero is Zero

Theorem

 * $\arctan 0 = 0$

Proof
By definition, $\arctan$ is the inverse of the tangent function's restriction to $\openint {-\dfrac \pi 2} {\dfrac \pi 2}$.

By Tangent of Zero:
 * $\tan 0 = 0$

As $0 \in \openint {-\dfrac \pi 2} {\dfrac \pi 2}$, we have $\arctan 0 = 0$ by the definition of an inverse function.