7 In this question you must show detailed reasoning.
- Show that the equation \(m \sec \theta + 3 \cos \theta = 4 \sin \theta\) can be expressed in the form
$$m \tan ^ { 2 } \theta - 4 \tan \theta + ( m + 3 ) = 0 .$$
- It is given that there is only one value of \(\theta\), for \(0 < \theta < \pi\), satisfying the equation \(m \sec \theta + 3 \cos \theta = 4 \sin \theta\).
Given also that \(m\) is a negative integer, find this value of \(\theta\), correct to \(\mathbf { 3 }\) significant figures.