In the story of "The Tell Tale Heart" is it right that the narrator is insane and use it as the evidence that he is not guilty of the crime? Why?...

If the narrator were truly insane, he probably would not
be able to relate the circumstances of the story or to feel anxiety at the visit of the
detective. Since the presence of the detective makes him increasingly uncomfortable, we
can surmise that he is feeling guilty and anxious about the possible discovery of his
crime. Despite his crimes, the narrator obviously feels that he is responsible and that
on some level he deserves punishment. The calm smiling demeanor of the detective
unhinges him, showing his paranoia and nervousness, until he can stand it no longer and
insists on tearing up the floorboards. This is his way of wanting to confess his crimes
and suffer the consequences, proving he understands the moral implications of his
actions, which proves he is sane.