First, let's calculate cos(67.5) and sin(67.5) using a calculator:

cos(67.5) ≈ 0.362
sin(67.5) ≈ 0.932

Now, we can substitute these values into the expression:

(cos^2(67.5) - sin^2(67.5)) - sin^2(225)
= (0.362^2 - 0.932^2) - 1
= (0.131044 - 0.868624) - 1
= -0.73758 - 1
= -1.73758

Therefore, the final result is approximately -1.73758.