f(x)=2sin(2x+π/6)+m+1
记t=2x+π/6,t∈[π/6,2π+π/6]
f(t)=2sin(t)+m+1
f(t)的单调递增区间为：
t∈[π/6,π/2]或t∈[3π/2,2π+π/6]
此时：
x∈[0,π/6]或x∈[2π/3,π]
即所求.