Question 17
Suppose $a$ is a real number such that the equation
$$
a\cdot(\sin x+\sin(2x))=\sin(3x)
$$
has more than one solution in the interval $(0,\pi).$ The set of all such $a$ can be written in the form $(p,q)\cup(q,r),$ where $p,$ $q,$ and $r$ are real numbers with $p\lt q\lt r.$ What is $p+q+r?$
$$
a\cdot(\sin x+\sin(2x))=\sin(3x)
$$
has more than one solution in the interval $(0,\pi).$ The set of all such $a$ can be written in the form $(p,q)\cup(q,r),$ where $p,$ $q,$ and $r$ are real numbers with $p\lt q\lt r.$ What is $p+q+r?$