السلام علیکم ورحمتہ اللہ
Originally Posted by Nitro Zeus
First of all, it is not necessary to pray tahajjud in the last third of the night, though better, but you can pray tahajjud any time in the night after Isha prayer till time for morning prayer.
"And Allah estimates the night and the day. He knows that you cannot count the (night), then He turned towards you with His mercy, now recite from Quran as much as is easy for you" [Surah Muzammil, Ayah 20]
As for as the last third of the night is concerned, there is a little difference of opinion among the scholars as you can see from above two comments. Some calculate from Isha prayer till morning (fajr) prayer, while others calculate it from Maghrib prayer till morning prayer. Both are fine, none is incorrect, but lets see what is meant by "Night", for if we could define the night, it becomes easy to calculate the last third of night as well.
In surah Al baqara, ayah number 187, Allah SWT says, ثُمَّ اَتِمُّوا الصِّيَامَ اِلَى الَّيۡلِۚ "......and then complete your fast untill the night." which means that night begins as soon as the sun sets because the fast is broken at sun set (Maghrib time). rather than the common notion that night begins when it gets complete darkness. In Arabic the word "Layl" is used for night.
Also the hadith further explains it:
“When the night enters from here [ie. the darkness of night on the Eastern horizon], and the day leaves from there [ie. on the Western horizon] and the sun has set, then one fasting should break his fast.” [Sahih Al-Bukhari]
Another reason to calculate the night from Maghrib is that the very timing for Isha Prayer (Night Prayer) is calculated from Maghrib (As First third of the night).
So the definition of night as mentioned by @SZ- Shaikh
"al-Misbah al-Munir, defines night as the time from sunset until the entry of the dawn prayer (fajr)", seems more accurate.
And Allah knows best.