y=sin(2x+π/6)-cos(2x+π/3)
=sin2x*(√3/2)+cos2x*(1/2)-cos2x*(1/2)+sin2x*(√3/2)
=√3sin2x
则单调增区间为
-π+2kπ≤2x≤2kπ
-π/2+kπ≤x≤kπ,
即为[-π/2+kπ,kπ]