Joseph's coat was more than just a piece of clothing. It was a catalyst for the events that unfolded. It set Joseph apart from his brothers, both in his father's eyes and in their own perception. When they got rid of Joseph, they sent the coat back to their father covered in blood, which was a cruel deception. This act started Joseph's journey of trials and eventually his rise to power in Egypt.
The coat of many colours was a central element. It was a physical manifestation of Joseph's special status in the family. His brothers' hatred towards him because of the coat led to his exile from his homeland. However, in the end, when Joseph revealed himself to his brothers in Egypt, the coat could be seen as a symbol of the journey he had been through. From being the favored son with a special coat to a powerful man who could now forgive his brothers who had once hated him for that very coat.