Let's simplify the expression step by step:

Recall the trigonometric identity: cos(2θ) = 1 - 2sin^2(θ)Rewrite the expression: 1 - 2sin^2(θ) - (1/ tan^2(θ) + 1) × sin^2(θ)Replace tan^2(θ) with 1/cos^2(θ):
1 - 2sin^2(θ) - (1/(1/cos^2(θ)) + 1) × sin^2(θ)Simplify the expression:
1 - 2sin^2(θ) - (cos^2(θ) + 1) × sin^2(θ)Expand the expression:
1 - 2sin^2(θ) - cos^2(θ)sin^2(θ) - sin^2(θ)Combine like terms:
1 - 3sin^2(θ) - cos^2(θ)sin^2(θ)Simplify further if needed, depending on the context of the problem.

With these steps, we simplified the given expression to 1 - 3sin^2(θ) - cos^2(θ)sin^2(θ).