said by LLigetfa:
he wants to run four sectors but he wants to run all four sectors on the same frequency.
Yes, he wanted to do that but obviously that won't work very well even with GPS sync and excellent front-to-back ratio sector antennas.
There would be interference contribution from 3 SMs (belonging to the other 3 APs) in every time slot. When some or all of those SMs are located at shorter distance from the tower than the target SM, noise may rise above expected RSSI.
People already suggested using a single omni antenna or 2x 180 degree sectors or a 1:4 splitter at each tower to meet his original desire to run one frequency per tower.
Using all three available frequencies at each tower to maximize his total wireless network capacity is just another option.