Using an excitable and unreliable narrator in "The Tell-Tale Heart" allows Edgar Allan Poe to

explore human psychology.

provide a calm perspective.

give the story a happy ending.

relate a powerful love story.

Based on the question given, the best answer for this would be:

To explore human psychology

Edgar Allan Poe has been known as an exquisite and unique writer in his in own way, he explores human psychology by creating a piece that would entitle to our thoughts and emotions.