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Simplify the expression (tanθ+cotθ)^2 - (tanθ-cotθ)^2 using algebra and trigonometric identities.

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(tanθ+cotθ)^2 - (tanθ-cotθ)^2
= (tan^2θ + 2 + cot^2θ) - (tan^2θ - 2 + cot^2θ)
= 4
because tanθ cotθ = 1

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