Solving for $z$ in $x=\frac y{2 \tan(z/2)}$

Question

I'm trying to solve for $z$ given $x=\dfrac y{2 \tan(z/2)}$.

Wolfram Alpha gives me the solution, but when I plug the formula into Excel it's not giving expected results at all - if I plug the same $x$ value into the formula it does not give me the $z$ that I originally started with.

Hopefully that's enough information to go off of; normally I frequent Stackoverflow. Thanks!

Answer 1

The solution is

$$2 \left(\pi c_1+\cot ^{-1}\left(\frac{2 x}{y}\right)\right)$$

where $c_1$ is an integer.

Doesn't this work for you?

Answer 2

We have

$$x=\frac y {2 \tan(z/2)} \iff \tan(z/2)=\frac y {2x} \iff z=2\arctan \frac y {2x}+2k\pi$$

provided that $z\neq 0 \quad x\neq 0$.