f(x)=sin(2x+φ)向左平移π/6后,函数为：f(x)=sin(2（x+π/6）+φ)=sin(2x+φ+π/3)
f（x）=sin(2x+φ+π/3),f（-x）=sin(-2x+φ+π/3)
偶函数有：f（x）=f（-x）于是：
有：sin(2x+φ+π/3)=sin(-2x+φ+π/3)
sin(2x+φ+π/3)-sin(-2x+φ+π/3)=0
和差化积：2sin（2x）cos（φ+π/3）=0
cos（φ+π/3）=0
所以：φ+π/3=kπ+π/2,k∈Z
于是最小值：φ=kπ+π/2 - π/3= π/2 -π/3=π/6