how to extract missing datetime interval in python

Question

I have a date dataframe where date contains 15 min of interval. I want to find the missing datetime interval. id should be copied from previous line but value should be nan '''

 date value id
   2021-12-02 07:00:00  12456677    693214
   2021-01-02 07:30:00  12456677  693214
   2021-01-02 07:45:00  12456677  693214
   2021-01-02 08:00:00  12456677 693214
   2021-01-02 08:15:00  12456665  693215
   2021-01-02 08:45:00  12456665  693215
   2021-01-03 09:00:00  12456666 693217
   2021-01-03 10:30:00  12456666   693217

expacted output is

date value id
   
   2021-01-02 08:30:00  NAN  693215
   2021-01-02 09:15:00 NAN    693217
   2021-01-03 09:30:00 NAN    693217
   2021-01-03 09:45:00 NAN    693217
   2021-01-03 10:00:00  NAN   693217

I am trying

df['Datetime'] = pd.to_datetime(df['date'])
df[ df['Datetime'].diff() > pd.Timedelta('15min') ]

but it is just giving a time after which date is missing. not the missing date and time.it showed me this output

date value id

   2021-01-02 08:15:00  12456665  693215
   2021-01-03 09:00:00  12456666 693217
   2021-01-03 10:30:00  12456666   693217

can some one please guide me how can I extract missing date and time? Thanks in advance