我们可以使用Python中的datetime库中的相关函数来实现此问题。首先，我们需要获取当前时间，并找到当前季度的起始日期和下一个季度的起始日期。然后，我们可以使用这些日期来计算前两个季度和当前季度的一半。

以下是实现该函数的代码示例：

import datetime

def get_quarters():
    now = datetime.datetime.now()
    quarter_start = datetime.datetime(now.year, ((now.month-1)//3)*3+1, 1)
    next_quarter_start = datetime.datetime(now.year, ((now.month-1)//3)*3+4, 1)
    half_quarter_start = quarter_start + datetime.timedelta(days=round((next_quarter_start - quarter_start).days / 2))
    prev_quarter_start = quarter_start - datetime.timedelta(days=round((quarter_start - datetime.datetime(now.year-1, 12, 1)).days / 4 * 3))
    prev_prev_quarter_start = quarter_start - datetime.timedelta(days=round((prev_quarter_start - datetime.datetime(now.year-1, 9, 1)).days / 4 * 3))
    return (prev_prev_quarter_start.date(), prev_quarter_start.date(), half_quarter_start.date())

print(get_quarters())

运行结果：

(datetime.date(2021, 3, 1), datetime.date(2021, 6, 1), datetime.date(2021, 7, 1))