Answer
$\theta=(2k+1)\pi$
Work Step by Step
We can first find all solutions in the interval $[0, 2\pi )$.
$\cos \theta +1=0$
$\cos \theta =-1$
$\theta=\pi$
Because $\cos \theta$ has period $2\pi$, we can add or subtract any multiple of $2\pi$ from $\pi$ and the equation would still hold:
$\theta=\pi+2 k \pi$ for any integer k
Factoring:
$\theta=(2k+1)\pi$ for any integer k
