What is the validity of Salman Rushdie's claim in "The Satanic Verses" that some verses of the Qur'an were revealed to approve of three deities in Mecca, and then abrogated with the claim that Satan was the one who whispered them to the Prophet without his knowledge? And what is the true account of what happened?

This narration is false and incorrect. Ibn Kathir and others have mentioned that it has not been authentically reported from the Prophet, peace be upon him, with a sound chain of transmission. Its falsity stems from several angles: its chains of transmission are weak, and the Prophet, peace be upon him, is infallible in conveying the message. Even if it were assumed to be authentic, scholars have stated that what was cast was into the hearing of the disbelievers and not from the tongue of the Messenger of Allah, peace be upon him.