Solution
Part A
For this case we can do the following:
![\sin \theta=\frac{\sqrt[]{3}}{2}](https://img.qammunity.org/2023/formulas/mathematics/college/xlbqkc4ononzdmzcay8b9sgbke7osana1w.png)
We can solve for theta and we have:
![\theta=\sin ^(-1)(\frac{\sqrt[]{3}}{2})=(\pi)/(3)+2\pi n](https://img.qammunity.org/2023/formulas/mathematics/college/t5j81nvu5utcwlqs8mjm4e5vrj77zseicg.png)
Then three possible angles are:

Part B
We have the following angle theta= 675º
And we want to find the value in radians and the find the secant so we can do this:

Solving for x we got:

And then we can find the secant and we have:
![\sec ((15\pi)/(4))=\sqrt[]{2}](https://img.qammunity.org/2023/formulas/mathematics/college/y1fc3qwqca1rwc8bu7yx9864fr3463u05s.png)