3.15: Parallel chords and the band between them

In this question, all lengths are in metres and all angles are in radians.

The diagram shows a circle with centre $O$ and radius $5$. The points $A$, $B$, $C$ and $D$ lie on the circumference of the circle. Angle $DOC = \theta$. Angle $AOD =$ angle $COB = 0.5$. The length of the minor arc $DC$ is $3.75$.