已知函数 f(x)=tanθ−tan(x+θ)1−2tan(x+θ)f\left( x\right) = \frac{\tan \theta - \tan \left( {x + \theta }\right) }{1 - 2\tan \left( {x + \theta }\right) }f(x)=1−2tan(x+θ)tanθ−tan(x+θ) 是 [−π2024,π2024]\left\lbrack {-\frac{\pi }{2024},\frac{\pi }{2024}}\right\rbrack[−2024π,2024π] 上的奇函数,则 tanθ=\tan \theta =tanθ= ( )A. 2B. -2C. 12\frac{1}{2}21D. −12- \frac{1}{2}−21