Verified answer

sin(thetta) = 1/3.

Now get arcsin to get the value of thetta.

thetta = arcsin(1/3)

then thetta = 19.47

So 2 * thetta = 38.94

cos(2thetta) = cos(38.94) = 0.7778 or 7/9

cos2θ = 1- 2(sinθ )^2 = 1 - 2(1/3)^2 = 7/9