I looked everywhere online and nobody properly explains how to solve trig inequalities, and i'm still stuck. This is the problem...

2sin

^{2}x > sinx , 0 < x < 2pi

I got to this point...

sinx(2sinx - 1) > 0

I then split the two expressions and solved, which gave me solutions of 0, pi, pi/6, and 5pi/6. It wants sin > 0 and sin > 1/2...so the final solution I ended up with was [0, pi] U [pi/6, 5pi/6] and it seemed right to me because this is where the expressions are positive but when I checked the given answer in the back of my packet, it did not match

The actual answer is [0] U [pi/6, 5pi/6] U [pi, 2pi)

How would I get this answer? Thanks in advance for the help