Question 1160399
<pre><font size=5>Did you make two typos?

((cos2θ+isinθ)^4*(cos3θ+isin3θ)^5)/(cos7θ+isin7θ)^3*(cosθ-isinθ)

I think you meant

((cos2θ+isin<b><font color="red">2</font></b>θ)^4*(cos3θ+isin3θ)^5)/(cos7θ+isin7θ)^3*(cosθ<font color="red"><b>+</b></font>isinθ)

If you meant a "2" and a "+" in those two places then I can show that the 
answer is cos3θ+isin3θ.  Otherwise it's a complicated mess.

Edwin</pre></font>