This is question 1c of a list of related items.
State the value(s) of $\theta$ in the range $0^\circ$ to $360^\circ$ so that the following is true: $$\tan\theta = \tan 20^\circ$$
Here is the answer (from the list of answers):
$$\theta = 20^\circ;\quad \theta=180^\circ+20^\circ=200^\circ$$
I am using the trig identity for tan, the one where $$\tan\theta = \tan(\theta-180^\circ)$$ If $\theta = 20^\circ$ for the question, then $\tan(\theta-180^\circ)$ is $\tan(20^\circ-180^\circ)$, which is $\tan(-160^\circ)$, which is taking me to a completely different direction than the solution.
I would appreciate it if someone could explain the steps of using this trig identity to determine which other angles have the same tan ratio as $20^\circ$.