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\sin(-\frac{1}{3}\pi )
Combine -\frac{\pi }{6} and -\frac{\pi }{6} to get -\frac{1}{3}\pi .
-\sin(\frac{1}{3}\pi )
Use the property \sin(-x)=-\sin(x).
-\frac{\sqrt{3}}{2}
Get the value of \sin(\frac{1}{3}\pi ) from trigonometric values table.