Suppose a is a real number such that the equation
a \cdot(\sin x+\sin (2 x))=\sin (3 x)
has more than one solution in the interval (0, \pi). The set of all such a that can be written in the form
(p, q) \cup(q, r),
where p, q, and r are real numbers with p<q<r. What is p+q+r ?
Answer Choices
A. -4
B. -1
C. 0
D. 1
E. 44