Prove the Identity:

$\displaystyle cot\;\theta - tan\;\theta = 2\;cot\;2\;\theta$

My Work:

$\displaystyle \frac{cos\;\theta}{sin\;\theta} - \frac{sin\;\theta}{cos\;\theta} = 2\;cot\;2\;\theta$

$\displaystyle \frac{cos^2\;\theta - sin^2\;\theta}{sin\;\theta\;cos\;\theta} = 2\;cot\;2\;\theta$

What do I do after I have all of this done?