How to find the intersection of this complex graph

Hey guys, I’ve attempted this question multiple times yet I can’t seem to get to the answer.

How do I find the intersect between the equations
y= sinxcos2x and y=1/2 - sin2xcosx

The mark scheme seemed to get the answer sin3x=1/2 and get exact answers.
However I keep getting 4sin^3x -3sinx + 1/2 = 0 which doesn’t allow me to get exact values. I used the double angle formula.
How do I manipulate this equation

4sin^3(x) -3sin(x) is equivlalent to -sin(3x). For an exact answer you generally want a multiple angle so combine (addition identity) the 2x and x to get 3x rather than splitting the 2x.

How did you do that step by step?
I’m a bit confused on how you managed to get 3x