3. If the equation $2 a \cdot 9^{\sin x}+4 a \cdot 3^{\sin x}+a-8=0$ has a solution, then the range of values for $a$ is ( ).
(A) $a \geqslant 0$ or $a \leqslant-8$
(B) $a \geqslant 0$
(C) $0 \leqslant a \leqslant \frac{8}{31}$
(D) $\frac{8}{31} \leqslant a \leqslant \frac{72}{23}$
3. D.

Let $t=3^{\sin x}$. Then $\frac{1}{3} \leqslant t \leqslant 3$. The original equation is $2 a t^{2}+4 a t+a$ $-8=0, a=\frac{8}{2(t+1)^{2}-1}$.
It is a monotonically decreasing function in $t \in\left[\frac{1}{3}, 3\right]$.
When $t=\frac{1}{3}$, the maximum value of $a$ is $=\frac{8}{2 \cdot\left(\frac{4}{3}\right)^{2}-1}=\frac{72}{23}$.
When $t=3$, the minimum value of $a$ is $=\frac{8}{2 \cdot 4^{2}-1}=\frac{8}{31}$.