Finding an exact expression for tan(pi/12)

The question:

Let $\displaystyle z = -2 + 2i$ and $\displaystyle w = -1 - \sqrt{3}i$.

i) Write z and w in polar form and thus write zw in polar form.

ii) Hence find an exact expression for $\displaystyle tan(\frac{\pi}{12})$

My attempt:

i) This is simple,$\displaystyle z = \sqrt{8}e^{\frac{3\pi}{4}i}; w = 2e^{\frac{-2\pi}{3}i} ; zw = 2\sqrt{8}e^{\frac{\pi}{12}i}$

ii) I'm not sure how to go about this. I notice that the argument of the previous answer matches that of this question. However, I do not know how to attempt it.

Any help would be great!