Double Angle Trig Question

Find the eact value of sin (2w), cos (2w), and tan (2w) using the double angle formulas. cos w = (-2/3), pi/2
Ok, I understand how to use the formulas to set up the problem, and I have the final answer as well I believe. However, I do not understand how to set up the problem. Could someone PLEASE show me how to do it? When you do so, please explain each little detail to me as to why you did what you did. I have not tackled a trig question in some time, so I want to fully understand every nuance of the issue. Thanks!

cos w = -2/3

sin^2 w + cos^2 w = 1
sin^2 w + (-2/3)^2 = 1
sin^2 w + 4/9 = 1
sin^2 w = 5/9
sin w = √5/3

sin 2w = 2 sin w cos w = 2(√5/3)(-2/3) = -4√5/9

cos 2w = cos^2 w - sin^2 w = (-2/3)^3 - (√5/3)^2 = 4/9 - 5/9 = -1/9

tan 2w = sin 2w/cos 2w = (-4√5/9)/(-1/9) = 4√5

In the second quadrant, sin w = sqrt[1 - cos^2 w] = sqrt(5)/3
sin (2w) = 2sin w cos w = 2[sqrt(5)/3](-2/3) = -4sqrt(5)/9
cos (2w) = 2cos^2 w - 1 = -1/9
tan (2w) = sin (2w)/cos (2w) = 4sqrt(5)