Let's simplify the given expression step by step:

cos(π/3 - α) * cos(π/3 - α) - cos^2 α

Using the double angle formula for cosine, we rewrite cos(π/3 - α) as:

cos(π/3 - α) = cos(π/3)cos(α) + sin(π/3)sin(α)
cos(π/3 - α) = (1/2)cos(α) + (√3/2)sin(α)

Substitute this back into the expression:

[(1/2)cos(α) + (√3/2)sin(α)] * [(1/2)cos(α) + (√3/2)sin(α)] - cos^2 α

Expanding the expression:

(1/4)cos^2 α + (√3/2)cos(α)sin(α) + (√3/2)cos(α)sin(α) + 3/4 sin^2 α - cos^2 α

Simplify further:

(1/4)cos^2 α + 3/2 cos(α)sin(α) + 3/4 sin^2 α - cos^2 α

Now, let's simplify the expression:

(1/4)cos^2 α + 3/2 cos(α)sin(α) + 3/4 sin^2 α - cos^2 α
= (1/4 - 1)cos^2 α + 3/2 cos(α)sin(α) + 3/4 sin^2 α
= -3/4 cos^2 α + 3/2 cos(α)sin(α) + 3/4 sin^2 α

Therefore, cos(π/3 - α) * cos(π/3 - α) - cos^2 α simplifies to -3/4 cos^2 α + 3/2 cos(α)sin(α) + 3/4 sin^2 α.