What is the limit $( 1 + 1/\tan(n) )^{\tan(n)}$

Question

What is the result of $\displaystyle \lim_{n\to \infty}\left(1+\frac{1}{\tan(n)}\right)^{\tan(n)}$ = ?
The limit does not exist as stated by Adam Rubinson.

Looks like the requested answer is e but then the question is wrong.
What is the correct question to give the answer e?

Did answered correctly. But I think this is some kind of typographical error.
This question appeared on a high school test and the intended question should have a small error.
What is the correct question to give the answer e changing only one value?

Answer 1

$$ \lim_{n\to\color{red}{\pi/2}}\left(1+\frac{1}{\tan(n)}\right)^{\tan(n)} = e$$

Answer 2

What is the correct question to give the answer $\mathrm e$?

$$ \lim_{n\to \infty}\left(1+\tan(1/n)\right)^{1/\tan(1/n)} =\ ? $$