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Complete this python program:
def TR3(rv):
assistant
#Here is the Python program you requested.

    """Induced formula: example sin(-a) = -sin(a)
    Examples
    >>> from sympy.simplify.fu import TR3
    >>> from sympy.abc import x, y
    >>> from sympy import pi
    >>> from sympy import cos
    >>> TR3(cos(y - x*(y - x)))
    cos(x*(x - y) + y)
    >>> cos(pi/2 + x)
    -sin(x)
    >>> cos(30*pi/2 + x)
    -cos(x)
    """
    from sympy.simplify.simplify import signsimp
    def f(rv):
        if (not isinstance(rv, TrigonometricFunction)):
            return rv
        rv = rv.func(signsimp(rv.args[0]))
        if ((rv.args[0] - (S.Pi / 4)).is_positive is ((S.Pi / 2) - rv.args[0]).is_positive is True):
            fmap = {cos: sin, sin: cos, tan: cot, cot: tan, sec: csc, csc: sec}
            rv = fmap[rv.func](((S.Pi / 2) - rv.args[0]))
        return rv
    return bottom_up(rv, f)