3 The angles \(\alpha\) and \(\beta\) are such that
$$\tan \alpha = m + 2 \quad \text { and } \quad \tan \beta = m$$
where \(m\) is a constant.
- Given that \(\sec ^ { 2 } \alpha - \sec ^ { 2 } \beta = 16\), find the value of \(m\).
- Hence find the exact value of \(\tan ( \alpha + \beta )\).