Let theta be an acute angle such that sin 5 theta = sin theta.
Compute tan 2 theta.
Since the sine of a reference angle in the 1st quadrant = the sine of the same reference angle in the second quadrant....we have that.....
(180 - 5theta) = theta
180 = 6 theta
180 / 6 = theta = 30°
tan (2 theta) = tan (60°) = sqrt (3)