Why is $\sin \theta$ just $\theta$ for a small $\theta$? When $\theta$ is very small, why is sin $\theta$ taken to be JUST $\theta$?

It's not just $\theta$.
What you observe is the fact that $\sin \theta$ and $\theta$ approach zero from either side of the number line at a pretty similar rate. This can be best demonstrated with a graph. 

You can see that they are about to overlap just at zero. So when $\sin \theta$ is approaching $0$ for some very very small $\theta$ we can approximate it as $\theta$.
Does this make sense?
