OK. I now know what kpi is: \(\displaystyle k \pi\). But I still don't see where \(\displaystyle \sin x \ne 0\) is relevant in your original post.

However, what you have written here is easy to understand. If \(\displaystyle \sin x \ne 0\), then \(\displaystyle x\) cannot be a multiple of \(\displaystyle \pi\). (Since the sine of all multiples of \(\displaystyle \pi\) is zero.) In other words:

\(\displaystyle \sin x \ne 0\)

\(\displaystyle \Rightarrow x \ne k\pi\), where \(\displaystyle k\) is an integer