The function is sinx(4sin2x - 1) = 0. Therefore, either sinx = 0 or 4sin2x - 1 = 0 to find all the zeros of
this function. For sinx, we know that it equals 0 at 0, pi and 2pi, (0 degrees, 180 degrees and 360 degrees).
For the other function, we can solve by writing it as 4sin2x = 1. Divide both sides by 4, and we get
sin2 x = 1/4. So sinx = 1/2 by taking the square root of both sides. The arcsin of 1/2 = pi/6 radians, that is, 30 degrees.
Since the sine is positive in quadrants I and II, we take the equivalent angle by finding (180 - 30) degrees,
which equals 150 degrees or (pi - pi/6), finding the common denominator get 5pi/6.
Final answer is 0, pi/6, 5pi/6, pi, 2pi or 0, 30 degrees, 150 degrees, 180 degrees and 360 degrees.