7 The angle \(\alpha\) lies between \(0 ^ { \circ }\) and \(90 ^ { \circ }\) and is such that
$$2 \tan ^ { 2 } \alpha + \sec ^ { 2 } \alpha = 5 - 4 \tan \alpha$$
- Show that
$$3 \tan ^ { 2 } \alpha + 4 \tan \alpha - 4 = 0$$
and hence find the exact value of \(\tan \alpha\).
- It is given that the angle \(\beta\) is such that \(\cot ( \alpha + \beta ) = 6\). Without using a calculator, find the exact value of \(\cot \beta\).