How do I find all solutions to $\sin(x+(\pi/7))=-1/\sqrt{2}$?

Question

I am stuck on the $\pi/7$ since it doesn't have known exact value-please help!

Answer 1

Hint. Let $y=x+\pi/7$. Solving $\sin y=-1/\sqrt2$ is easy because you know the exact values, and then solving for $x$ is easy because you don't need to know any exact values!