No, the problem _is_ solved by adding an extra day in February. The
web page just forgot to mention that every 100 years a leap year is
omitted. Thus, the extra day is Febrary 29th.
A year isn't exactly 365 days long (as most people already know). The
purpose of leap years is to approximate the actual length of a year.
Without leap years the northern hemisphere would have cold "summers"
and warm "winters" one day. (This already happened a long time ago
when calendars weren't as good as they are now.)
Leap seconds solve a mostly independent problem: A day isn't 86400
seconds long. Positive or negative leap seconds are inserted once in a
while because the sun should be shining at noon and not at midnight.
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