c# - When a sprite is rotating to follow an angle, how to prevent it from reversing direction after a point?

Below is a section of my code which handles a player's sprite rotating towards an angle after a user touches the screen:

touchState = TouchPanel.GetState();

Vector2 touchPosition;

if (touchState.Count > 0)
{
   touchPosition = new Vector2(touchState[0].Position.X, touchState[0].Position.Y);
   targetPosition = Math.Atan2(player.Position.X - touchPosition.X, player.Position.Y - touchPosition.Y);

if (angle_radians < targetPosition)
{
    angle_radians += 2 * fps;

}

if(angle_radians > targetPosition)
{
    angle_radians -= 2 * fps;
}

player.Angle = angle_radians * -1;
}

The problem I'm having is that when the angle goes past a certain point (I believe 3.15 radians?), the logic no longer functions correctly and the sprite reverses direction in a 360 circle until it meets the target position again.

I know there is something I'm missing from this logic, and I can see the problem, but I'm not sure how to approach handling it.

How would I prevent the sprite from reversing direction?

Thanks

EDIT: I tried the solution below but I only receive a positive number from 0-6 for angle_distance, what have I done wrong?

            if (touchState.Count > 0)
            {
                touchPosition = new Vector2(touchState[0].Position.X, touchState[0].Position.Y);
                targetPosition = Math.Atan2(player.Position.X - touchPosition.X, player.Position.Y - touchPosition.Y);
                angle_distance = targetPosition - angle_radians + Math.PI;

                angle_distance = angle_distance - Math.Floor(angle_distance / 2 / Math.PI) * 2 * Math.PI;

                if (angle_distance < 0)
                {
                    angle_radians -= 2 * fps;
                }

                if (angle_distance > 0)
                {
                    angle_radians += 2 * fps;

                }

                player.Angle = angle_radians * -1;
            }

EDIT: I now realise my mistake, correct solution is below

if (touchState.Count > 0)
                {
                    touchPosition = new Vector2(touchState[0].Position.X, touchState[0].Position.Y);
                    targetPosition = Math.Atan2(player.Position.X - touchPosition.X, player.Position.Y - touchPosition.Y);


                    angle_distance = targetPosition - angle_radians + Math.PI;
                    angle_distance = angle_distance - Math.Floor(angle_distance / 2 / Math.PI) * 2 * Math.PI;

                    if (angle_distance < Math.PI)
                    {
                        angle_radians -= 2 * fps;
                    }

                    if (angle_distance > Math.PI)

                    {
                        angle_radians += 2 * fps;
                    }

                    player.Angle = angle_radians * -1;
                }

Answer

First, find the signed distance between the two angles:

dist = targetAngle - currentAngle + pi
dist = dist - floor(dist / 2 / pi) * 2 * pi - pi

If it's negative, then subtract from the current angle to reach the other angle in the shortest time, if it's positive, then add to it.