In a $\triangle ABC$, $\angle B = \frac{π}{3}$ and $\sin A \cdot \sin C = m$. Then we have to find all possible values of $m$.

What I did was wrote $C=\frac{2π}{3}-A$. Hence

$$\sin A \cdot \sin(\frac{2π}{3}-A)=m$$. 

Further I wrote $\sin(\frac{2π}{3}-A)$ as 

$$\sin C \cdot \cos D - \sin D \cdot \cos C$$

Later I assumed $\sin A=t$ but I got a polynomial of degree 4. Which I was unable to solve.