The direction ratios of two lines are given by a+b+c=0, 2ab+2ac-bc=0. Then the angle between the lines is 

$\begin{array}{l}a+b+c=0\mathrm{.......}\left(1\right)\\ 2ab+2ac-bc=0\\ 2a(b+c)-bc=0\\ -2a{(b+c)}^2-bc=0\\ \Rightarrow (b+2c)(2b+c)=0\end{array}$

$\begin{array}{l}\Rightarrow c=-2b\left(or\right)-\frac{b}{2}\\ Ifc=-2bthena:b:c=1:1:-2\\ Ifc=-\frac{b}{2}thena:b:c=1:-2:1\\ \cos \theta =\frac{|a_1{a}_2+b_1{b}_2+c_1{c}_2|}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2}}=\left|\frac{-3}{6}\right|=+\frac{1}{2}\Rightarrow \theta =\frac{\pi }{3}\end{array}$