$\tan z = \frac{\sin(z)}{\cos(z)}, \cos(z), \sin (z) \ \forall z \in \mathbb{C}$
Injectivity means: $f(x)=f(y) \Rightarrow x=y$
so i think all intervals of the form $[0,u< 2\pi]$ are good. And I also think this is wrong.
Dose somebody see how to find the correct regions.
Tell me. Please
V