omega doesnt have to be ei*(2pi/7) it can be ei*(4pi/7)
Correct. I just went for the simplest option!
Could you tell me how you get from the last but one line to the last one, (without the use of a calculator). ?
I cheated and used a calculator (well, Mathcad's calculation facilities).
Thinking about it further, I made the last few lines of the derivation of q more complicated than necessary. Going back a few lines from the end we can do the following: