Drei Gleichen from German is translated as "three identical". In reality, the castles, are not the same. Only located on the identical hills.
They never belonged to the same owner and were united by the natural phenomenon. According to legend, in 1231 there was a ball lightning, which set fire to all three castles. In memory of this event, a medieval show "Dreinschlag" is held. During it, all three castles burn with a controlled fire and a big firework ends the show. The next date is August 22, 2020. Information about this event in German https://www.dreinschlag-drei-gleichen.de/.
It is curious that the first shows in 2002 - 2003 created emergency situations on the autobahn, so now it is blocked for several hours.
Mühlburg Castle (704 year)
Parking: N 50 52.131 E 10 49.660, then uphill on foot.
Bus: Mühlberg (Kreis Gotha), Drei Gleichen, use bahn.de.
Visiting is possible from 10 to 16 (to 18 on Saturday and Sunday).
Gleichen Castle (1034 year)
Parking: N 50 52.962 E 10 50.442, then uphill on foot.
Bus: Freudenthal, Drei Gleichen, use bahn.de.
Visiting is possible from 10 to 18
Veste Wachsenburg Castle (930 year)
Parking: N 50 51.526 E 10 52.584, in front of the entrance to the castle
The hotel is located in the castle (https://www.wachsenburg.com/). The place is not touristic, but you can walk around the castle.