Chapter 9.3, Problem 41ES

As shown in the accompanying figure, suppose that an angle $\theta$ is bisected using a straightedge and compass to produce ray $R_1,$ then the angle between $R_1,$ and the initial side is bisected to produce ray $R_2.$ Thereafter, rays $R_3,R_4,R_5,\mathrm{...}$ are constructed in succession by bisecting the angle between the preceding two rays. Show that the sequence of angles that these rays make with the initial side has a limit of $\theta /3.$