It's 1/3
draw a equilateral triangle, connect O (center of the circle ) to two angles of the triangle
now there's a angle formed at O, which is 120 degrees
imagine when you move two lines you just connected, when they become closer, the angle between them become smaller, then the chord is less than the side of the triangle
In contrast, if you expand the same angle to a degree that bigger than 240, the chord is smaller than the side of the triangle
so the angler is between 120 to 240, the range is 240 - 120 = 120
there's 360 degrees around, so use 120/360=1/3