import math


def angle_closeness(a, b, error):
    """Determine the closeness of two angles, in radians, if they are witin the error closeness, in radians.

    # Simple angles.
    >>> angle_closeness(1, 1.1, .2)
    True
    >>> angle_closeness(1, 1.2, .1)
    False

    # Negative angles.
    >>> angle_closeness(-1, -1.1, .2)
    True
    >>>
    angle_closeness(-1, -1.2, .1)
    False

    # Zero angles.
    >>> angle_closeness(-.1, .1, .3)
    True
    >>> angle_closeness(.1, -.1, .3)
    True
    >>> angle_closeness(.1, -.1, .1)
    False
    >>> angle_closeness(-.1, .1, .1)
    False

    # Angles near PI.
    angle_closeness(3.1, 3.0, .2)
    True
    angle_closeness(-3.1, -3.0, .2)
    True
    angle_closeness(-3.1, 3.1, .2)
    True
    angle_closeness(3.1, -3.1, .2)
    True
    angle_closeness(3.1, 3.0, .05)
    False
    angle_closeness(-3.1, -3.0, .05)
    False
    angle_closeness(-3.1, 3.1, .05)
    False
    angle_closeness(3.1, -3.1, .05)
    False
    """
    if abs(a - b) < error:
        return True
    else:
        if a < 0:
            a += math.pi * 2
        elif b < 0:
            b += math.pi * 2
        return abs(a - b) < error