已知不等式f=根号3cos-sin是奇函数,则tanθ等于?

f(x)= √3cos(3x-θ)-sin(3x-θ)
=2[√3/2 cos(3x-θ)-1/2sin(3x-θ)]
=2[sin(π/3) cos(3x-θ)-cos(π/3)sin(3x-θ)]
=2sin(π/3-3x+θ)
∵f(x)是奇函数
∴π/3+θ=kπ,θ=kπ-π/3(k∈Z)
∴tanθ= tan(kπ-π/3)=- √3