I just saw this update and need to add some detail I think.

     Africa/Cairo observes DST in 2016 from July 7 to the end of October.
     Guess October 27 and 24:00 transitions. (Thanks to Steffen Thorsen.)
     For future years, guess April's last Thursday to October's last
     Thursday except for Ramadan.

Now, this may change next year but the current story from Egypt's government is that they will not be implementing DST until the end of Ramadan going forward.