What degree of elevator deflection is required to takeoff?
It depends. Mostly on two parameters:


What is the position of the center of gravity? A more forward position would require a bigger downforce at the tail, so deflection angles would be bigger. On the 777-200, c.g. positions from 14% to 44% of MAC are allowed.
What is the trim setting of the stabilizer? Depending on the setting, more or less deflection is needed to set the whole horizontal tail to the right downforce for rotation.


Further parameters are flap settings, take-off mass, rotation speed and desired rate of rotation, but the first two are the most important.

Since I do not have the official Pilot's Operating Handbook for the Boeing 777, the virtual version has to do. Sadly, it contains very little information. The more seedy corners of the internet have maybe more substantial content, but here you are on your own.

The Boeing 777 has a computer based weight and balance system, called Accuload, which will compute the proper take-off trim setting, therefore, no discrete values can be given. With the recommended trim setting, the pilot will apply forward pressure on the control column until roatation speed ($v_R$), relaxing control forces to neutral for smooth rotation.

If you would take off with the trim setting for cruise, the elevator would need to be deflected by approx. -10° (trailing edge up) in a simulation with typical parameters. Please note that this is not the regular take-off procedure, and the actual deflection angles are much smaller.