We must make good use of our brain and mind. Indeed, we must make them sharp as if by frequent honing so that they will help us in finding the truth. Why did Sankara master all the sastras, all the arts, all the sciences, Sankara who thought the world was Maya? Why did he ascend the "sarvajna-pita" (seat of omniscience)?
I said Nyaya was also known as Tarka, "Anviksiki". We learn from the Sankara-Vijaya that the Acarya mastered Nyaya or Anviksiki, Kapila Maharsi's "Kapilam" (Sankhya), Patanjali's Yoga-sastra ("Patanjalam"), Kumarilabhatta's Mimamsa ("Bhatta-sastra").
Anviksikyaiksi tantre paracitiratula
Kapile kapi lebhe
Pitam Patanjalambhah paramapi viditam
Advaita embraces even those sastras that apparently do not speak about it. That is why I am speaking about all such sastras though I am called "Sankaracarya". Non-dualism inheres dualism, qualified non-dualism, Saivism, Vaisnavism and so on. It enfolds even those systems that are critical of it. Advaita does not state that other systems are totally false. If it opposes them it is only to the extent needed to counter their argument against itself. It concedes them the place they deserve.
For a general background, please see here