If a 3yr old's tantrums get her what she wants they will obviously continue. Special attention and treats when she is being good could perhaps help and will be as important, or more so, than being firm when the tantrums do occur. Letting her scream for an hour last night, difficult as it must have been, could well have a positive effect as long as that approach is continued, she certainly won't scream for an hour twenty times a day. Be cruel to be kind perhaps but give her all the love in the world when she stops.
Wish your daughter good luck, not an easy problem to cope with.