I'm trying to solve the second order D.E: sin(theta)y'' -cos(theta)y' + 2ysin(theta)^3 = 0 using the substitution x = cos(theta). According to Wolfram Alpha, there exists a trigonometric solution but my working does not lead me towards it. Here is what I have:

Please excuse the bad handwriting - it seems to be exacerbated by scanning my working in!

Thanks in Advance.