4 The acute angles \(\alpha\) and \(\beta\) are such that
$$2 \cot \alpha = 1 \text { and } 24 + \sec ^ { 2 } \beta = 10 \tan \beta \text {. }$$
- State the value of \(\tan \alpha\) and determine the value of \(\tan \beta\).
- Hence find the exact value of \(\tan ( \alpha + \beta )\).