exact trig values, help!

Arcsin(theta) = Arcsin(1/3) = theta = 19.47 degrees          then just use calculator to find cot(19.47) = 2.828

Sorry ...didn't see 'EXACT' in your post

sin(theta) = 1/3           cos^2 (theta) =  (1-sin^2)

                                                          = 1-1/9 = 8/9

                                    cos theta = sqrt (8/9)=  2sqrt2  /  3 

COT(theta) = cos/sin   =   (2sqr2 / 3) /  1/3  =     2sqrt2 / 3  x  3/1  = 2 sqrt2