How I Perform Insert and select

INSERT INTO (Id, Dates.date_type, Dates.date_displayed)
SELECT (
    SELECT Id, 'Start_date' AS date_Type, Start_date AS date_displayed
    FROM T_Dates
    UNION ALL
    SELECT Id, 'End_date' AS date_Type, End_date AS date_displayed
    FROM T_Dates
    UNION ALL
    SELECT Id, 'Set_date' AS date_Type, Set_date AS date_displayed
    FROM T_Dates
) AS T

SET DATEFORMAT mdy;

CREATE TABLE #T_Dates (ID INT IDENTITY(1,1), [Start_date] DATETIME, [End_date] DATETIME, [Set_date] DATETIME, [Another_date] DATETIME)

INSERT INTO #T_Dates ([Start_date], [End_date], [Set_date], [Another_date] )
VALUES('10/1/2014', '10/6/2014', '10/2/2014', '10/8/2014'),
('10/7/2014','10/4/2014','10/3/2014', '10/6/2014'),('10/17/2014','10/14/2014','10/13/2014', '10/9/2014')


CREATE TABLE #Dates(ID INT IDENTITY(1,1), Old_ID INT, Date_Type VARCHAR(30), Date_Displayed DATETIME)

INSERT INTO #Dates (Old_ID, [Date_Type], [Date_Displayed])
SELECT ID AS Old_ID, [Date_Type], [Date_Displayed]
FROM (
    SELECT *
    FROM #T_Dates
    ) AS pvt
UNPIVOT( [Date_Displayed] FOR [Date_Type]  IN([Start_date], [End_date], [Set_date], [Another_date])) as unpvt

SELECT *
FROM #Dates

DROP TABLE #T_Dates
DROP TABLE #Dates

ID  Old_ID  Date_Type   Date_Displayed
1   1   Start_date  2014-10-01 00:00:00.000
2   1   End_date    2014-10-06 00:00:00.000
3   1   Set_date    2014-10-02 00:00:00.000
4   1   Another_date    2014-10-08 00:00:00.000
5   2   Start_date  2014-10-07 00:00:00.000
6   2   End_date    2014-10-04 00:00:00.000
7   2   Set_date    2014-10-03 00:00:00.000
8   2   Another_date    2014-10-06 00:00:00.000
9   3   Start_date  2014-10-17 00:00:00.000
10  3   End_date    2014-10-14 00:00:00.000
11  3   Set_date    2014-10-13 00:00:00.000
12  3   Another_date    2014-10-09 00:00:00.000