Find a if the equation has a solution

Question

If this equation has a solution, then 'a' is equal to

1. 
2. 

3. 

4. None of these

How should I proceed in this problem?

Answer 1

As suggested by Daniel Fischer, $-1\le \dfrac{x^2}{3}-4x+13\le1$ gives $x\le 6$ is one of the possibilities. If we put $x=6$ in the given equation, we get $\sin \dfrac{a}{6}=1$. Thus $a={3(4n+1)\pi}$.