On Phalgun Krishna 2nd, Rama's army seized the gates of Lanka. Angada proceeded as Rama emmisary on a peace mission to Ravana's court. However, any peace proposal was rejected by Ravana and the next day (Phal.Kr. 3rd), Rama-Ravana war commenced.
The great war spanned 13 days and concluded on Phalgun Krishna Amavasya, with the death of Ravana. The very next day, Chaitra Shuddha 1st was celebrated as a Victory Day. This tradition still continues to be a New-Years's Day and is marked by hoisting flags.
15th November 7292 B.C was then Phalguna Amavasya. Valmiki states that Ravan came out for the last battle on the Amavasya day (Yudh. 93/66) and was killed. In the description of the battle, Sage Valmiki writes, "Kosala's nakshatra Vishakha is aspected by Mars" (Yudh. 103/37). The annual motion of Mars is 191.405 degrees. In 14 years, it will progress by 159.58 degrees. At the time of Rama's exile, Mars was at 303 deg. 159 deg. added to this provides Mars at 102 deg. in Pushya. From Pushya Mars could cast its fourth-sight on Vishakha. So, the calculations presented so far seem to be correct. It also shows Valmiki's minute observations and time recording capabilities
Thus, the date of the last battle of the War is 15th November 7292 B.C.