integrate [sin2x] from 0 to 2pi where [.] means greatest integer function

If the value of sin 2x is between 0 to 1, then [.] = 0
If the value of sin 2x is between -1 to 0, then [.] = -1.
sin 2x is negative in range : (pi/2,pi) and (3pi/2,2pi)
Hence, answer is : -1(pi-pi/2) -1(2pi - 3pi/2)
Answer : -pi
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thanku sir