Prince snuck in to a private box during the first act of American Ballet Theatre’s premiere of “The Nutcracker” to see Misty Copeland perform at the Brooklyn Academy of Music on Thursday. He has a special relationship with Copeland, the company’s only African-American dancer. She appeared in Prince’s music video “Crimson and Clover” and gave a special performance onstage at Madison Square Garden during his concert last week. Prince had previously invited her onstage to dance at a concert in Nice, France.