If $ \sin\theta + \cos\theta = \frac 1 2$, what does $\tan\theta + \cot\theta$ equal? A SAT II question asks:
If $ \sin\theta + \cos\theta = \dfrac 1 2$, what does  $\tan\theta + \cot\theta$ equal? 
Which identity would I need to solve this? 

Hint
$$\sin\theta+\cos\theta=\frac{1}{2} \implies \left( \sin\theta+\cos\theta \right)^2 = \frac{1}{4} \iff \color{blue}{\cos\theta\sin\theta} = \cdots$$
and
$$\tan\theta+\cot\theta = \frac{\sin\theta}{\cos\theta}+\frac{\cos\theta}{\sin\theta} = \frac{\cos^2\theta+\sin^2\theta}{\cos\theta\sin\theta}= \frac{1}{\color{blue}{\cos\theta\sin\theta}} = \cdots$$
