IB Math HL Trigonometry Test 4 2015 P2 Q2

The diagram shows a circle with centre \(O\), radius \(r\), and \(\angle AOB=\theta\) radians. The minor segment \(AB\) is shaded.

1. Find \(\theta\) if the ratio of the minor arc length to the major arc length is \(1:5\).[2]
2. Find \(\theta\) if the ratio of the shaded area to the non-shaded area is \(1:5\).[4]