<s>[INST] If $x \leq y \leq z$, and both sides of the equation are defined, then $\frac{\sin x + \sin y + \sin z }{\cos x + \cos y + \cos z} = \tan y.$ Show that if $x$, $y$, and $z$ are consecutive terms of an arithmetic sequence, with $x \leq y \leq z$, and both sides of the equation are defined, then 
$$\frac{\sin x + \sin y + \sin z }{\cos x + \cos y + \cos z} = \tan y.$$

I have no idea how to even start this problem, I'm stuck.  Solutions are greatly appreciated. 
 [/INST] Let $x=y-d$ and $z=y+d$ with $d>0$. Then
\begin{align*}
\frac{\sin x + \sin y + \sin z }{\cos x + \cos y + \cos z}& = \frac{\sin (y-d) + \sin y + \sin (y+d) }{\cos (y-d) + \cos y + \cos (y+d)}\\
& = \frac{2\sin y \cos d + \sin y}{2 \cos y \cos d + \cos y}\\
& = \tan y.
\end{align*}
</s>