Prove that cos (2π/13)+ cos (6π/13) + cos (8π/13)= (sqrt(13)-1)/4
Since and , it follows that
But (with similar results for and ). Also, (with similar results for the other two products and ).
Putting all that together, you find that
Now let and It follows from the above calculations that and Eliminate T between those equations to get , a quadratic with solutions Now all that remains for you to do is to figure out why the square root must have the plus sign.