Let's simplify the expression:

= (8sin^4(3π/20) - 8cos^4(3π/20)) / sin(4π/5)

Now, recall the trigonometric identity: sin^2θ + cos^2θ = 1.

Since we are dealing with sin^4 and cos^4, we can square this identity:

(sin^2θ + cos^2θ)^2 = 1
sin^4θ + 2sin^2θcos^2θ + cos^4θ = 1

Therefore, 2sin^2θcos^2θ = sin^4θ + cos^4θ - 1

Now, let's rewrite the expression using the identity we just derived:

= 8(sin^4(3π/20) + cos^4(3π/20) - 1) / sin(4π/5)

= 8(sin^4(3π/20) + cos^4(3π/20) - 1) / (2sin(2π/5)cos(2π/5))

= 8(sin^4(3π/20) + cos^4(3π/20) - 1) / (2 2 sin(π/5) * cos(π/5))

= 8(sin^4(3π/20) + cos^4(3π/20) - 1) / (4sin(3π/20))

At this point, it is difficult to simplify the expression further without specific values for sin(3π/20) and cos(3π/20).