How do we find period of [Sin3x] where [. ] is greatest integer function.

HiSin3x lies between -1&1 with period 2pi/3.For the values of sin3x between 0 and 1,[sin3x] will be 0 and for sin3x between 0 and -1,it will be =-1.If u draw its graph,u will see that [sin3x] takes value of 0 in between o and pi/6 and then -1 from pi/6 to pi/3 and again 0 from pi/3 to pi/2.Since [sin3x] got repeated after pi/3,so the period of [sin3x] is pi/6.HOPE THIS HELPS.CHEERS!!