tan²θ = sin²θ / cos²θ.

Numerator:
tan²θ − sin²θ
= (sin²θ / cos²θ) − sin²θ
= sin²θ (1/cos²θ − 1)
= sin²θ ((1 − cos²θ)/cos²θ)
= sin²θ (sin²θ / cos²θ)
= sin⁴θ / cos²θ.

Denominator:
2 + tan²θ + cot²θ
= 2 + (sin²θ / cos²θ) + (cos²θ / sin²θ).

Using identity:
tan²θ + cot²θ = (sin⁴θ + cos⁴θ) / (sin²θ cos²θ).

So denominator becomes:
2 + (sin⁴θ + cos⁴θ) / (sin²θ cos²θ).

Since 2 = 2sin²θcos²θ / (sin²θcos²θ),

Denominator = (2sin²θcos²θ + sin⁴θ + cos⁴θ) / (sin²θcos²θ).

But 2sin²θcos²θ + sin⁴θ + cos⁴θ = (sin²θ + cos²θ)² = 1.

So denominator = 1 / (sin²θcos²θ).

Therefore expression = (sin⁴θ / cos²θ) × (sin²θcos²θ / 1)
= sin²θ.