If tan α = m / (m + 1), tan β = 1 / (2m + 1), then find the value of α + β.

tan α = m / (m + 1), tan β = 1 / (2m + 1)

tan(α + β) = (tan α + tan β) / (1 − tan α · tan β)

= ( (m / (m + 1)) + (1 / (2m + 1)) ) / (1 − (m / (m + 1)) · (1 / (2m + 1)) )

= (2m² + m + m + 1) / (2m² + m + 2m + 1 − m)

= (2m² + 2m + 1) / (2m² + 2m + 1)

⇒ tan(α + β) = 1

∴ α + β = π/4