Trigonometry Problem

I've been working on this question for a while, but I can't come up with a defininitive solution. Can you guys help with it a bit? Thanks!

So let's $x \in (0^{\circ}, 90^{\circ})$ such that

$\frac{\sin(60^{\circ}-x)}{\sin(x)} = \frac{\sin(10^{\circ})}{\sin(150^{\circ})}$

Find all such values of x.

The problem with this is you can't really use direct relations, and I think I might get messy trying to combine everything together. I thought about using negatives, but wouldn't that be just heading further down the path?

Thanks!