If m²(sin θ − 1) + n²(sin θ + 1) = 0, where 0 < θ < π/2, then what is (m² + n²)cos θ − (m² − n²)cot θ equal to?

From m²(sin θ − 1) + n²(sin θ + 1) = 0: sin θ(m² + n²) = m² − n², so sin θ = (m² − n²)/(m² + n²). Then (m² + n²)cos θ − (m² − n²)cot θ = (m² + n²)cos θ − (m² − n²)·cos θ/sin θ = cos θ[(m² + n²) − (m² − n²)/sin θ] = cos θ[(m² + n²) − (m² + n²)] = 0. (Since (m² − n²)/sin θ = (m² + n²).)