I'd use a radio control type servo motor.
They are readily available in various size & power ratings, from tiny to very high torque & typically operate from around 5V
The position is set by the width (duration) of a pulse, usually between 1.5 to 2.5mS over the full range of movement.
That can come from microcontroller or just a 55 timer with the appropriate values around it & switching in resistors to change the position.
You could either attach the servo shaft to the end of the hinge, or put it below the display carrier and use a wire pushrod from a servo arm to part way up the back of the display, to give the appropriate range of movement.
For info & reference, these are around the extremes - the little ones have nine grams force at one cm from the shaft centre, the big one 25Kg at 1cm from the shaft centre; 25 Kg-cm torque, almost 2.5NM
**broken link removed**
Or a typical mid-range type, around 3Kg-cm which should be fine for what you need:
Just search ebay for "RC Servo" to find other examples.
ps. Operating time for 90' movement is typically under a quarter of a second.