If you can keep a tiny little data file around, you only need to figure out the epoch seconds for one invocation of the script. Just add (60 * 60 * 24) seconds to it once a day, and generate the new sleep value with a simple subtraction statement.
I'd do something like:
# run operation
# get timestamp from file
# add 60 * 60 * 24 to it
# write new timestamp to file
# subtract current seconds from timestamp
# sleep for result seconds
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