Angles between chords and radius lines of concentric circles

Figure 1
Figure 1

Applying the sine rule to Figure 1:

\[\begin{align} \frac{\sin \theta_{2}}{R_{1}} & = \frac{\sin ( \pi - \theta_{1} )}{R_{2}} \\ & = \frac{\sin \theta_{1}}{R_{2}} \\ \sin \theta_{2} &= \frac{R_{1}}{R_{2}} \sin \theta_{1} \end{align}\]