First, we need to use the trigonometric identity relating sine and cosine of complementary angles:

sin(arcsin(x)) = x = cos(arccos(x))

Therefore, we have:

arcsin(1/3) = arccos(2/3)

Now we can substitute these into the original expression:

cos(arcsin(1/3) - arccos(2/3))

= cos(arccos(2/3) - arccos(2/3))

= cos(0)

= 1

Therefore, the value of the expression is 1.