These days are the following:
The Third of Tishrei. This is the day on which Gedaliah ben Achikam was slain and the ember of Israel that remained was extinguished, causing their exile to become complete.
The Tenth of Tevet. This is the day Nebuchadnezzar, the wicked, the King of Babylon, camped against Jerusalem and placed the city under siege.
The Seventeenth of Tammuz. Five tragedies took place on this day:
a) The Tablets were broken;
b) In the First Temple, the offering of the daily sacrifices was nullified;
c) [The walls of] Jerusalem were breached in [the war leading to] the destruction of the Second Temple;
d) Apostmos, the wicked, burned a Torah scroll; and
e) He erected an idol in the Temple.