Verify and prove that, how and why  "Formula to find the Order of rotation" is :
​(360^°/Angle of rotation).
​

{Please don't provide any web - link or certified answer... I want only experts answer} 

The number of times a figure fits into itself in one complete rotation is called the order of rotational symmetry.

If A° is the smallest angle by which a figure is rotated so that rotated from fits onto the original form, then the order of rotational symmetry is given by 360°/A° [A° < 180°]

It can be only varified 

Rectangle (clockwise)

We observe that while rotating the figure through 360°, it attains original from two times i.e., it looks exactly the same at two positions. Thus, we say that the rectangle has a rotational symmetry of order 2.

Equilateral triangle (clockwise):

We observe that at all 3 positions, the triangle looks exactly the same when rotated about its center by 120°.

Letter B (clockwise):

We observe that only at one position the letter looks exactly the same after taking one complete rotation.

Windmill (anticlockwise):

We observe that if we rotate it by one – quarter, at 4 positions, it looks exactly the same. Therefore, the order of rotational symmetry is 4.