Answer
$θ=\frac{\pi}{3}+2n\pi$ and $θ=\frac{5\pi}{3}+2n\pi$, where $n$ is an integer.
Work Step by Step
$4~cos~θ=1+2~cos~θ$
$2~cos~θ=1$
$cos~θ=\frac{1}{2}$
The period of $cos~θ$ is $2\pi$. The solutions in the interval: $[0,2\pi)$ are:
$θ=\frac{\pi}{3}$ and $θ=\frac{5\pi}{3}$
Now, add multiples of $2\pi$ to each of the solutions:
$θ=\frac{\pi}{3}+2n\pi$ and $θ=\frac{5\pi}{3}+2n\pi$, where $n$ is an integer.
