What is wrong with my attempt of $0 \lt w \lt \frac{\pi}{6}$ then $w \csc w$ is? 
For $0 \lt w \lt \frac{\pi}{6}$,  the value of  $ w  \csc w $ is
A) less than $ \frac{\pi}{6}$
B) greater than $ \frac{\pi}{6}$
C) less than $\frac{\pi}{3}$
D) greater than $ \frac{\pi}{3}$

I know from L'hospital rule that $ \lim_{h\to 0} \dfrac{h}{\sin h} = 1 $
and $\sin \frac{\pi}{6} = 0.5 $, thus
$ w  \csc w $ goes from $1$ to $\frac{\pi}{3}$. (Open interval)
Thus answer should be (B and C) greater than $\frac{\pi}{6}$ and less than $\frac{\pi}{3}$.
But the answer is only C.

Per the comments, this appears to be a case of looking for the "best answer," whatever that this. If this was given to you by an instructor rather than taken from a textbook, you may wish to bring it up with them.
