I'd like to propose bytians - a "new" angular measurement system which uses 256 divisions of a circle.
Full circle - 256 bytians
Half circle - 128 bytians
Right angle - 64 bytians
Diagonal - 32 bytians
We lose nice triangular angles, where 60° = 42.66... bytians. More exactly, this would be 128/3 bytians.
(Also, this has to have been done before)