When considering tangent, it is hopefully no surprise that at it's most basic, we can just use \(\tan(2\theta)=\dfrac{\sin(2\theta)}{\cos(2\theta)}\):

From this equation you can basically substitute in the double sine formula and any of the double cosine formulas: \[\solve{ \tan(2\theta)&=&\dfrac{2\sin\theta\cos\theta}{\cos^2\theta-\sin^2\theta}\\ \\\tan(2\theta)&=&\dfrac{2\sin\theta\cos\theta}{1-2\sin^2\theta}\\ \\\tan(2\theta)&=&\dfrac{2\sin\theta\cos\theta}{2\cos^2\theta-1} }\]