A circle centered at $O$ has radius $1$ and contains the point $A$. Segment $AB$ is tangent to the circle at $A$ and $\angle AOB = \theta$. If point $C$ lies on $\overline{OA}$ and $\overline{BC}$ bisects $\angle ABO$, find the value of $OC$. The original answer is in the form \frac{k}{1+m\sin(\theta)}, please give the value of k + m.

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