Let m1 and m2 be the slopes of two lines.
∴ tan θ = |

m1−m2

1+m1m2

|
Here tan θ =

1

3

, m1 = m , m2 = 2m

1

3

= |

m−2m

1+m(2m)

| ⇒

1

3

= |

−m

1+2m2

|
⇒ |1 + 2m2| = 3|m| ⇒ 2|m|2 – 3|m| + 1 = 0
⇒ 2|m|2 – 2|m| – |m| + 1 = 0 ⇒ (2|m| – 1) (|m| – 1) = 0
⇒ |m| =

1

2

,1 ⇒ m = ± 1 , ±

1

2

Slope of the two lines are 1 , 2 ; - 1 , - 2 ;

1

2

, 1 ; −

1

2

, - 1