Draw the sine wave, at least two cycles-worth, so you can see what sin(t) looks like.
Mark where t = pi/3, and draw the vertical line up to the sine wave.
Now move along to the right, marking every spot where the sine wave is at the same height. This will occur, on the way back down, in the first half of the first cycle. By symmetry, this must be at pi - pi/3 = (3/3)pi - (1/3)pi = (2/3)pi.
The sine wave will be negative in the second half of the first cycle, so...
Oh.
Okay, so the third and fourth values I listed previously were wrong. Argh!
The sine wave will be positive again in the first half of the
next cycle, so add pi/3 and 2pi/3 to 2pi to get their values, etc, etc. Then do the division to solve the original equation.
Sorry!