1.(2023•福建模拟)函数f(x)=2sin(ωx+π6)(ω∈R)f(x)=2\sin (\omega x+\frac{\pi }{6})(\omega \in R)f(x)=2sin(ωx+6π)(ω∈R)恒有f(x)⩽f(2π)f(x)\leqslant f(2\pi )f(x)⩽f(2π),且f(x)f(x)f(x)在[−π6[-\frac{\pi }{6}[−6π,π3]\frac{\pi }{3}]3π]上单调递增,则ω\omegaω的值为((( )))