x∈[-π/3,π/3]
(π/3-x) ∈[0,2π/3]
当(π/3-x) ∈[0,π/2)时
tan(π/3-x)∈[0,+∞]
当(π/3-x) ∈(π/2,2π/3] 时
tan(π/3-x)∈(-∞,-根号3]
所以函数的值域是(-∞,-根号3]∪[0,+∞]