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

Combining the LHS: cosθ[(1 + sinθ) + (1 − sinθ)]/[(1 − sinθ)(1 + sinθ)] = 2cosθ/cos²θ = 2/cosθ = 2secθ. So 2secθ = 4, giving secθ = 2, hence cosθ = 1/2 and sinθ = √3/2. Then tanθ = √3 and cotθ = 1/√3. So tan²θ + cot²θ = 3 + 1/3 = 10/3.