If tan⁻¹(x/(2x+4)) + tan⁻¹(x+2/(x+4)) = π/4, find the value of x.

tan⁻¹(x/(2x+4)) + tan⁻¹(x+2/(x+4)) = tan⁻¹((x/(2x+4) + (x+2)/(x+4)) / (1 - (x/(2x+4))((x+2)/(x+4)))) = tan⁻¹(2x/(2x+4)) = π/4
Therefore we get 2x/(2x+4) = 1, which implies 2x = 2x+4, which gives x = -2. However, this value of x makes the argument of tan⁻¹ negative, leading to a solution outside the range of arctan.