if sinA+sin2A=1 THEN EVALUATE cos12A+3cos10A+3cos8A+cos6A+2cos4A+2cos2A-2

You can find one answer for this pretty easily if you first think about what angle 'a' must be for sin(a) + sin(2a) = 1. Then substitute that value for 'a' into the second equation. But there is a second answer that is a bit more difficult to determine - I can come up with a numerical approximation for this second answer but as yet haven't figured out a "nice" way to get a closed form solution.