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this is about the 3rd time this has come up, so again,
since sin^2x = 1-cos^2x
you have
1 - cos^2x - ā2 cosx = cos^2x + ā2 cosx + 2
2cos^2x + 2ā2 cosx + 1 = 0
(ā2 cosx + 1)^2 = 0
cosx = -1/ā2
x = Ļ Ā± Ļ/4 + 2kĻ