Let's use the trigonometric identity:

cos^2(x) + sin^2(x) = 1

Given that sin^2(x) = 2/3, we can solve for cos^2(x) using this identity:

cos^2(x) + 2/3 = 1
cos^2(x) = 1 - 2/3
cos^2(x) = 3/3 - 2/3
cos^2(x) = 1/3

So, cos^2(x) = 1/3.

Now, let's find tan^2(x) using the identity:

tan^2(x) = sin^2(x) / cos^2(x)
tan^2(x) = (2/3) / (1/3)
tan^2(x) = 2

Therefore, cos^2(x) = 1/3, tan^2(x) = 2, and sin^2(x) = 2/3.