cos(2a) = sin(3a)

cos(2a) = sin(a)cos(2a) + sin(2a)cos(a)

cos(2a) - sin(a)cos(2a) = sin(2a)cos(a)

cos(2a) * (1 - sin(a)) = 2sin(a)cos(a)cos(a)

cos(2a) * (1 - sin(a)) = 2sin(a) * cos(a)^2

cos(2a) * (1 - sin(a)) = 2 * sin(a) * (1 - sin(a)^2)

cos(2a) * (1 - sin(a)) = 2 * sin(a) * (1 - sin(a)) * (1 + sin(a))

1 - sin(a) = 0 is a solution

sin(a) = 1

a = pi/2 + 2pi * k

cos(2a) = 2 * sin(a) * (1 + sin(a))

cos(a)^2 - sin(a)^2 = 2 * sin(a) + 2 * sin(a)^2

1 - 2 * sin(a)^2 = 2 * sin(a) + 2 * sin(a)^2

0 = 4 * sin(a)^2 + 2 * sin(a) - 1

sin(a) = (-2 +/- sqrt(4 + 16)) / 8

sin(a) = (-2 +/- 2 * sqrt(5)) / 8

sin(a) = (-1 +/- sqrt(5)) / 4

sin(a) = (sqrt(5) - 1) / 4 , -(1 + sqrt(5)) / 4

a = arcsin((1/4) * (sqrt(5) - 1)) + 2pi * k , arcsin((-1/4) * (sqrt(5) + 1)) + 2pi * k

a = pi/10 + 2pi * k , 9pi/10 + 2pi * k , 13pi/10 + 2pi * k , 17pi/10 + 2pi * k

a = pi/10 , pi/2 , 9pi/10 , 13pi/10 , 17pi/10