To simplify the expression, we can use the trigonometric identity:

cos(2x) = cos^2(x) - sin^2(x)

Let's apply this identity to the denominator first:

cos(2 * 67.5°) = cos^2(67.5°) - sin^2(67.5°)

We can use the half-angle formula to find the values of cos(67.5°) and sin(67.5°):

cos(67.5°) = cos(45° + 22.5°) = cos(45°)cos(22.5°) - sin(45°)sin(22.5°) = (sqrt(2)/2)(sqrt(2 + sqrt(2))/2) - (sqrt(2)/2)(sqrt(2 - sqrt(2))/2) ? 0.3827

sin(67.5°) = sin(45° + 22.5°) = sin(45°)cos(22.5°) + cos(45°)sin(22.5°) = (sqrt(2)/2)(sqrt(2 + sqrt(2))/2) + (sqrt(2)/2)(sqrt(2 - sqrt(2))/2) ? 0.9239

Substituting these values into the identity gives:

cos(2 * 67.5°) = cos^2(67.5°) - sin^2(67.5°) ? -0.5858

Now let's simplify the numerator:

2sin(15°)cos(15°) = sin(30°) = 1/2

Substituting these values into the original expression gives:

(2sin15° cos15°)/(cos2 67,5°- sin2 67,5°) = (1/2)/(-0.5858) ? -0.4273

Therefore, the simplified value of the expression is approximately -0.4273.