Question 46
Find all values of the real parameter $a$ such that the image of the function
$$
f(x)=\frac{\sin^{2} x-a}{\sin^{3} x-\left(a^{2}+2\right) \sin x+2}
$$
contains the interval $\left[\frac{1}{2}, 2\right]$.
$$
f(x)=\frac{\sin^{2} x-a}{\sin^{3} x-\left(a^{2}+2\right) \sin x+2}
$$
contains the interval $\left[\frac{1}{2}, 2\right]$.