Tg(pi/2+3α) * tg(pi-3α) + 1 - sin^2α / 1 - cos^2α

Using trigonometric identities:

tg(pi/2+3α) = cot(3α)

tg(pi-3α) = -tg(3α) = -tan(3α)

1 - sin^2α = cos^2α

1 - cos^2α = sin^2α

Therefore, the expression simplifies to:

cot(3α) * (-tan(3α)) + cos^2α / sin^2α

= -1 + cos^2α / sin^2α

= cos^2α / sin^2α - 1

= (cosα / sinα)^2 - 1

= (cotα)^2 - 1

= cot^2α - 1.

Therefore, the final expression is cot^2α - 1.