Solve:

sin3xcosx = cos3xsinx

Here's what I've done so far:

sin3xcosx = cos3xsinx

sin3xcosx - cos3xsinx = 0

sin(2x+x)cosx - cos(2x+x)sinx = 0

(sin2xcosx + cos2xsinx)cosx - (cos2xcosx - sin2xsinx)sinx = 0

Here's where I'm stuck. Should I distribute the cosx and sinx on either side? Or plug in the sin2x/cos2x double angle identities?

Any help is appreciated!