Find all $x$ between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ such that $1 - \sin^4 x - \cos^2 x = \frac{1}{16}.$  Enter all the solutions, separated by commas.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find all $x$ between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ such that $1 - \sin^4 x - \cos^2 x = \frac{1}{16}.$  Enter all the solutions, separated by commas.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-\frac{5 \pi}{12}, -\frac{\pi}{12}, \frac{\pi}{12}, \frac{5 \pi}{12}
Find all $x$ between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ such that $1 - \sin^4 x - \cos^2 x = \frac{1}{16}.$  Enter all the solutions, separated by commas.
train