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Sinx + sin2x = 1
2 sin 3x/2  cos x/2  = 1
cos x/2 = 1 / (2 sin 3x/2 )

cos x + cos 2x =  2 cos x/2 cos 3x/2  substitute value of cos x/2 from above
   = cos 3x/2  / sin 3x/2  =  COT 3x/2
put x=(pi/2) in the given equation..
it satisfies the eqn.. thus put x=pi/2 in cosx + cos2x..
There are two solutions to the problem. x = 20.353445 deg and 90 deg. At x=90 deg. cosx+cos2x= -1= cot 3Pi/4 . at x=20.353445 deg, cosx+cos2x=1.695 = cot 30.53 deg . So cot 3x/2 satisfies both solutions.
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