to solve the equation apply the inverse function of the cos on both sides
[tex]\begin{gathered} \cos ^{-1}(\cos \theta)=\cos ^{-1}(-1) \\ \theta=\cos ^{-1}(-1) \\ \theta=180 \end{gathered}[/tex]Using the unit circle there is only one solution over the given interval.
Answer
[tex]\theta=180[/tex]