This can be simplified using the product-to-sum identities:

cos (A) cos (B) - sin (A) sin (B) = cos (A + B)

Therefore, the given expression can be simplified to:

cos (pi/8 + 3pi/8) = cos (pi/2) = 0

So, Cos (pi/8) Cos (3pi/8) - sin (pi/8) sin (3pi/8) is equal to 0.