Trig: sin (-165) using sum/difference identities

sin(-165), without calculator, using the sum and difference identities

Any help appreciated :)

sin (-120 + -45)
sin(-120)*cos(-45) + cos(-120)*sin(-45)
((-Root3/2))*((Root2)/2) + (-1/2)*((-Root2)/2)
(-Root6)/4 + (Root2)/4
(-Root6 + Root2)/4

So, it should end up looking like this:

√2-√6
———
4