Proving that $\tan(z)$ is bijective

Question

Prove: $\tan(z)$ is bijective over the domain/codomain$$\{z\in\mathbb{C}: -\pi/2<Re(z)<\pi/2\}\to \mathbb{C}\setminus\{i,-i\}$$ I had no problem showing injectivity of the tangent function but as soon as I started dealing with surjectivity I had a problem. I was thinking about using the Intermediate value theorem in a way but not sure how to apply it in this case.