13. Equation
$$
1-3 \sin \theta+5 \cos 3 \theta=0(0<\theta<2 \pi)
$$

has ( ) different solutions.
(A) 2
(B) 4
(C) 5
(D) 6
(E) 8
13. D.

Let $f(x)=5 \cos 3x, g(x)=3 \sin x-1$, as shown in the figure
12.

Obviously, $f(x)$ and $g(x)$ have six intersection points.