Assuming that by 'epoch time' you mean time_t, you don't need to convert to some other form. Since time_t is a lying liar and pretends every day is exactly 86400 seconds long, you can just do some /'s and %'s to find which fit in the same day and the highest for the day.
(of course, because of the undefined behavior around leap seconds, you can't really be sure whether % 86_400 == 0 is actually 00:00:00 or 23:59:60, but I think most systems repeat the 86399th instead. And since you can't tell anyway, it probably doesn't matter)
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