How do I simplify inverse functions trig?

Okay, i don't really know where to start

"simplify completely. your answers should not contain trigonometric or inverse trigonometric functions

$\displaystyle sin(Arcsin2/3+Arccos\sqrt3/2)$

So I think I should solve for $\displaystyle Arcsin2/3$ and $\displaystyle Arcos\sqrt3/2$, then add them to get one number and take the sin of that number.

Would that be the steps?

however, I don't know how to solve for $\displaystyle Arcsin2/3$ and $\displaystyle Arccos\sqrt3/2$