Remember that cosine is positive in the first and fourth quadrants.
To get the angle that's in the first quadrant, we solve for Theta as following:
![\begin{gathered} \cos \theta=\frac{\sqrt[]{3}}{2} \\ \\ \rightarrow\theta=\cos ^(-1)(\frac{\sqrt[]{3}}{2}) \\ \\ \Rightarrow\theta=30 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/b0d5gg4qm10wmp3z0np1xfz006iw40torp.png)
To get the angle in teh fourth quadrant, we substract the calculated angle from 360°

Therefore, the two angles we're looking for are 30° and 330°