Solve $\sin x+\cos x+\tan x+\csc x+\sec x+\cot x=-2$ in the interval $0
Solve $$\sin x+\cos x+\tan x+\csc x+\sec x+\cot x=-2$$ from $0<x<2\pi$.
Could you find the most elegant solution? Does it factorize?

This might be considered an extended comment of lab bhattacharjee's answer above. 
The roots of the factored form are 
$(\cos x + \sin x)(\cos x + 1)(\sin x +1) = 0$
which gives
$\cos x = -\sin x$. The 2 solutions are $\dfrac{3\pi}{4}$ and $\dfrac{7\pi}{4}$;
$\cos x = -1$. The solution is $\pi$;
$\sin x = -1$. The solution is $\dfrac{3\pi}{2}$.
So on the interval $0 < x < 2\pi$, you have the solutions $\dfrac{3\pi}{4}, \pi, \dfrac{3\pi}{2}, \dfrac{7\pi}{4}$.
EDIT: Thanks to lab bhattacharjee for noticing which values will be undefined if evaluated in the original equation. The the only solutions that work are $\dfrac{3\pi}{4}$ and $\dfrac{7\pi}{4}$.
