At the back of means inside (or attached to) something and at the rear of it.
The person farthest from the screen is at the back of the theater.
The last people to arrive are at the back of the line.
The vertical stabilizer is at the back of the airplane.
In back of means behind.
The trash is kept in back of the store. (It is outside, behind the store.)
The trash is kept at the back of the store. (It is inside, far from the front.)
The chair is in back of the television. (Someone in the chair can't see the television.)
The chair is at the back of the television. (This doesn't make sense in English because the chair would have to be inside, or attached to the rear of the television.)