We have a rectangle that is rotating by its center from $0$ to $360$ degrees. This rectangle rotation starts in $0$ degrees when we know all four rectangle points. We also know the angle we want to rotate the rectangle.
What I need is a formula for these points when rectangle is rotated.
When you rotate the point $(x,y)$ through an angle of $\theta$ (radians, not degrees) about the origin the new position is $$ (x \cos\theta - y \sin\theta\ , \quad x\sin\theta + y\cos\theta). $$
(https://en.wikipedia.org/wiki/Rotation_matrix)
If the center of the rectangle is not at the origin, translate the center to move it there, rotate, then translate back.