IB Math HL Trigonometry Test 5 2016 P2 Q5

A rope \(ACDB\) of length \(3.6\text{ m}\) is tied at endpoints \(A,B\) of a straight rod and passes over a disc of radius \(0.6\text{ m}\). The rod passes through the centre \(O\), and \(\angle CAO=\angle DBO=\theta\), measured in radians.

1. Explain why \(\angle COD=2\theta\), and hence show that \(\cot\theta+\theta=3\).[5]
2. Find \(\theta\), correct to four decimal places.[2]