Shirley, I give you one trick first for you to try.

1. Draw a line vertically downwards from C to meet BA at right angles. Call this point E.

2. Draw a horizontal line leftwards from D to meet line CE at right angles. Call this point F.

You will realise that

- angle ABC is θ
- angle BEC is 90°
- angle BCE, upon calculation, is (90° - θ)
- angle FCD, upon calculation, is θ
- angle CFD is 90°

Consider triangles BCE and CDF and use "toa cah soh" to obtain BE and FD. Note that FD is equal in length to EA, so that

BE + FD
= BE + EA
= BA

You should get AB = 4 cos θ + sin θ in a matter of time.

If you still need help later, I post everything.