2sin(2x+π/6)-1=0
sin(2x+π/6)=1/2
2x+π/6=2kπ+π/6或2x+π/6=2kπ+5π/6
得x=kπ或x=kπ+π/3
故函数的零点集合是｛x|x=kπ或x=kπ+π/3,k为整数｝