Hello! I have to evaluate:

I decided to start by getting rid of the imaginary part in the denominator. If $\displaystyle w=(2e^{it}-1)^3$ then $\displaystyle \overline{w}=(2e^{-it}-1)^3$.$\displaystyle \int_0^{2 \pi} \frac{e^{4e^{2it}}(2ie^{it})}{(2e^{it}-1)^3}~dt$

HOWEVER! $\displaystyle w \overline{w}=(2e^{it}-1)^3(2e^{-it}-1)^3=(4-2e^{-it}-2e^{it}+1)^3$. Unfortunately, this hasn't removed the imaginary ppart from the denominator.

What's going wrong?