The sum of all the elements in the range of
\[
f(x)=\operatorname{sgn}(\sin x)+\operatorname{sgn}(\cos x)
+\operatorname{sgn}(\tan x)+\operatorname{sgn}(\cot x),
\]
where
\[
x\neq \frac{n\pi}{2},\ n\in\mathbb{Z},
\]
and
\[
\operatorname{sgn}(t)=
\begin{cases}
1, & t>0 \\
-1, & t<0
\end{cases}
\]
is: