write the expression in polar form: \(\displaystyle \frac{(2+2i)(1+\sqrt{3})}{(3i)(\sqrt{12}-2i)}\)

Here is my work:

\(\displaystyle \frac{(2+2i)(1+\sqrt{3})}{(3i)(\sqrt{12}-2i)}\)

that is

\(\displaystyle \frac{2(1+i)2(cis\frac{\pi}{3})}{3cis(\frac{\pi}{2})(2\sqrt{3}-2i)}\)

and that becomes:

\(\displaystyle \frac{2\sqrt{2}cis(\frac{\pi}{4})2(cis\frac{\pi}{3})}{3cis(\frac{\pi}{2})2(\sqrt{3}-i)}\)

and then

\(\displaystyle \frac{2\sqrt{2}cis(\frac{\pi}{4})2(cis\frac{\pi}{3})}{3cis(\frac{\pi}{2})2(\sqrt{3}-i)}\)

\(\displaystyle \frac{2\times 2 \times \sqrt{2}(cis(\frac{\pi}{4}))(cis(\frac{\pi}{3}))}{3\times cis(\frac{\pi}{2})\times 2\times cis(\frac{11\pi}{12})}\)

anyway the correct answer is -1 I get the absolute value wrong can anyone spot my error.?