Question 11.4.5

Given that \begin{align*} \sin(\theta + \phi) &= \sin\theta\cos\phi + \cos\theta\sin \phi\\ \cos(\theta + \phi) &= \cos\theta\cos\phi - \sin\theta\sin\phi \end{align*} find $\tan(\theta + \phi)$ in terms of $\tan\theta$ and $\tan\phi$. Show hint