How don I find all solutions to $\sec(3 \theta)=1$ with $\theta$ in degrees?

Question

Sorry. I don't have the Greek theta symbol in my device

Answer 1

\begin{align*} \sec(3 \theta) = 1 &\iff \frac{1}{\cos(3 \theta)} = 1 \\ &\iff 1 = \cos(3 \theta)\\ &\iff 3 \theta = 2 \pi n \text{ for some } n \in \mathbb{Z}\\ &\iff \theta = \frac{2 \pi n}{3} \text{ for some } n \in \mathbb{Z} \end{align*}

These values are in radians. To convert them to degrees multiply by $\frac{180}{\pi}$.