Hmm, I used x=tanT, but it didn't work for some reason.
My "r" seems to be different from yours too.
r=cos3θ+sin3θ3cosθsinθIs what I get (so do you ignoring the typo)
Then divide everything by cos³:
r=1+tan3θ3tanθsec2θSo squaring r gives
r2=9(1+tan3θ)2tan2θsec4θWhich turns to x²(1+x²)/(1+x³)².
x²/(1+x³)² is pretty obious but I haven't been able to do much about the x^4/(1+x³)²
Except for make an algebraic error and evaluate it as a standard form ^.^
But ignoring that...hm.
Though I did this at like three in the morning, so I've probably just done something dumb...