hello,
I'm having a few difficulties with this question.

a. Calculate the moment of the 90N force about the point O for the condition θ = 15°.

b. Determine the value for θ when the moment about O is zero.

c. Determine the value for θ when the moment about O is a maximum.

You need to resolve F perpendicular and parallel to OA. Can you not do b and c? They seem easier. Can you tell me what conditions the answers to b and c should obey with relation to OA, even if you cannot work out the angle?

In case you haven't noticed, I'd like you to do your own work, but I'm happy to help you along.