Simplify the expression: (cos 6B + cos 2B) / (sin 6B + sin 2B)

The relevant identities are:

For the numerator, we have $\cos 6B + \cos 2B$. Let $X = 6B$ and $Y = 2B$.

For the denominator, we have $\sin 6B + \sin 2B$. Let $X = 6B$ and $Y = 2B$.

Cancel out the common terms 2 and $\cos(2B)$ (assuming $\cos(2B) \neq 0$).

Using the identity $\frac{\cos \theta}{\sin \theta} = \cot \theta$:

The left-hand side simplifies to $\cot(4B)$. The question asks to show that it equals $\tan(4B)$.
Since $\cot