On circle \(O\), points \(C\) and \(D\) are on the same side of diameter \(\overline{AB}\), \(\angle AOC = 30^\circ\), and \(\angle DOB = 45^\circ\). Find the ratio of the area of the smaller sector \(COD\) to the area of the circle. The original answer is in \(\frac{k}{m}\) format, please give the value of k + m.

Let's think step by step and output the final answer within \boxed{}.
user