∵函数f(x)=Asin(wx+π/6)的最大值为2
∴A=2
又∵图像相邻两对称轴之间的距离为π/3
∴T/2=π/3
即T=2π/3
又∵最小正周期为：T=2π/w
即2π/w=2π/3
∴w=3
∴函数为：f(x)=2sin(3x+π/6)
即f(2π/3)=2sin(3*2π/3+π/6)
=2sin(2π+π/6)
=2sin(π/6)
=1