Why is the value of sin 4pi over 3 equal to negative root 3 over 2

4π/3 = ~1.3π, which is between 1π and 3π/2 and therefore is an angle in the 3rd quadrant (image shows it). The absolute value of the angle will be the same as its opposite in the trigonometric circle, π/3, which is a well known angle with a sine of √(3)/2. But with that a angle in the 3rd quadrant, both sine and cosine will be negative, so the final value of sin(4π/3) = -√(3)/2