ANSWER
θ = 0
EXPLANATION
The secant function is the inverse of the cosine function:
[tex]\sec \theta=\frac{1}{\cos \theta}[/tex]So we can rewrite the equation:
[tex]\begin{gathered} \sec \theta=1 \\ \frac{1}{\cos \theta}=1 \end{gathered}[/tex]Solving for theta:
[tex]\begin{gathered} \cos \theta=1 \\ \theta=\arccos (1) \end{gathered}[/tex]This means that we have to find an angle for which its cosine is 1. If theta is between 0 and 360 degrees, there's only one solution - one angle whose cosine is 1: θ = 0.
See the graph of cos(θ):
