First off, just wanted to say that you've got a great attitude here.

What you've said so far is perfect. Labelling the midpoint of AB as M is good. You've correct identified that the angle you want to find is the angle CMD.

Now the rest of the answer reveals more and more hints as you progress through the post, so don't read the entire answer at once; read it sentence by sentence, if an idea pops out at you, stop reading immediately and try it out then return and continue reading if it wasn't successful.

Now, you want to do something involving $\cos$ of that angle, so that either calls for using the cosine rule on the triangle you mentioned, CDM or by finding some embedded right-angled triangle and using basic trigonometry. Now, because it's a STEP question, you typically want to use information you uncovered in the previous part, namely the length of PD. Here are some guiding questions:

1. What happens if you consider that embedded right angle triangle DMP?

2. Can you use some basic trigonometry on the angle CMD or equivalently PMD?

3. Hopefully something involving the length PD?

4. Are there any other lengths you might need to find?

5. If so, are they straighforward to compute?

[Remark: it's very hard to give a small push in the right direction here, because it's a one-liner answer]