If cosθ/(1 - sinθ) + cosθ/(1 + sinθ) = 4, then which of the following is the value of (tan²θ + cot²θ)?

Combine LHS: cosθ[(1+sinθ + 1-sinθ)]/[(1-sinθ)(1+sinθ)] = 2cosθ/cos²θ = 2/cosθ = 4. So cosθ = 1/2, hence sinθ = √3/2 (assuming acute). Then tanθ = √3, cotθ = 1/√3. tan²θ + cot²θ = 3 + 1/3 = 10/3.