Let $m_1$ and $m_2$ be the slopes of two lines. ∴ tan θ = $\left|\frac{m_1-m_2}{1+m_1m_2}\right|$ Here tan θ = $\frac{1}{3}$ , $m_1$ = m , $m_2$ = 2m $\frac{1}{3}$ = $\left|\frac{m-2m}{1+m(2m)}\right|$ ⇒ $\frac{1}{3}$ = $\left|\frac{-m}{1+2m^2}\right|$ ⇒ |1 + $2m^2$| = 3|m| ⇒ $2\left|m\right|^2$ – 3|m| + 1 = 0 ⇒ $2\left|m\right|^2$ – 2|m| – |m| + 1 = 0 ⇒ (2|m| – 1) (|m| – 1) = 0 ⇒ |m| = $\frac{1}{2},1$ ⇒ m = ± 1 , ± $\frac{1}{2}$ Slope of the two lines are 1 , 2 ; - 1 , - 2 ; $\frac{1}{2}$ , 1 ; $-\frac{1}{2}$ , - 1