Solve: sin2xsinx - cos2xcosx = 1, x domain [-pi, pi].

Answer 1

or
cos2xsinx - sin2xcosx = -1
compare this to
cos(A+B) = cosAcosB - sinAsinB
looks like somebody expanded cos(2x+x)

so cos 3x = -1 , (I know cos π = -1)
3x = π
x = π/3
so for your given domain, x = ± π/3