Power Series of Sine of Odd Theta

Theorem
Let $r \in \R$ such that $\size r < 1$.

Let $\theta \in \R$ such that $\theta \ne m \pi$ for any $m \in \Z$.

Then:

Proof
From Euler's Formula:
 * $\map \exp {i \theta} = \cos \theta + i \sin \theta$

Hence:

It is noted that when $\theta$ is a multiple of $\pi$ then:
 * $1 - 2 r \cos 2 \theta + r^2 = 1 - 2 + 1 = 0$

leaving the undefined.