def truncate_quarter(datetime):
    '''
    Truncates the datetime to the first day of the quarter for this date.

    :params datetime: an initialized datetime object
    :return: `datetime` with the month set to the first month of this quarter
    :rtype: :py:mod:`datetime` datetime object
    '''
    datetime = truncate(datetime, 'month')

    month = datetime.month
    if 1 <= month <= 3:
        return datetime.replace(month=1)
    elif 4 <= month <= 6:
        return datetime.replace(month=4)
    elif 7 <= month <= 9:
        return datetime.replace(month=7)
    elif 10 <= month <= 12:
        return datetime.replace(month=10)