'Everytime she starts we try to calm her down and reason with her. '

Don't!!! Ignore her, send her to her room, leave the room yourself if needs be but don't pamper her outbursts. If she didn't grow out of them at the toddler stage and that has always been your tactic to handle them it sounds like she may have missed out on learning how to cope with frustrations (which is what toddler tantrums are all about...its there window to learn to calm down to cope with all the difficult situations life throws at us, we naturally want to fix it whether its to keep them happy or keep them quiet but it backfires on us in the long run). She will no doubt go to extra lengths at first but put your foot down and be strong and get the message through loud and clear that she will NOT get your attention until she being reasonable...and then give her lots.

She will have learnt from not having the tv etc, but what she will have learnt is that next time she must shout louder/behave worse to get her own way.

(If you ever feel like backing down imagine her in a few years time behaving the same way...she'll be bigger than you and have better stunts to pull...could you cope with her behaviour then?)