You could expand the fractions with , and so on.
After expanding, the demoninator will be a 2 i Sin[~], which is a multiple of Pi. The numerator is Exp[i~], which could you rewrite in a+ ib if you want to do.
Just try to expand the first solution with and you will see it works.
The original problem statement was to find all the solutions of . I simplified this equation to equal and then wrote in polar form as .
I then simplified to the equation for .
Obviously, isn't a solution, so I came up with the other 4 using that format, but I wasn't able to simplify them. But then I wondered if they need to be simplified. Thanks for your help.