- In this question you must show all stages of your working.
\section*{Solutions relying on calculator technology are not acceptable.}
Given that the first three terms of a geometric series are
$$12 \cos \theta \quad 5 + 2 \sin \theta \quad \text { and } \quad 6 \tan \theta$$
- show that
$$4 \sin ^ { 2 } \theta - 52 \sin \theta + 25 = 0$$
Given that \(\theta\) is an obtuse angle measured in radians,
- solve the equation in part (a) to find the exact value of \(\theta\)
- show that the sum to infinity of the series can be expressed in the form
$$k ( 1 - \sqrt { 3 } )$$
where \(k\) is a constant to be found.