I3.3 In Figure 2, a circle at centre $O$ has three points on its circumference, $A, B$ and $C$. There are line segments $O A, O B, A C$ and $B C$, where $O A$ is parallel to $B C$. If $D$ is the intersection of $O B$ and $A C$ with $\angle B D C=(2 \beta-1)^{\circ}$ and $\angle A C B=\gamma^{\circ}$, find the value of $\gamma$.
$\begin{array}{l}\angle A O B=2 \gamma^{\circ}(\angle \text { at centre twice } \angle \text { at circumference }) \\ \angle O B C=2 \gamma^{\circ}(\text { alt. } \angle, O A / / C B) \\ \gamma^{\circ}+2 \gamma^{\circ}+(2 \beta-1)^{\circ}=180^{\circ}(\angle \mathrm{s} \text { sum of } \triangle) \\ 3 \gamma+111=180 \\ \gamma=23\end{array}$