[tex]\begin{gathered} \text{Slope of the first line m1=3} \\ let\text{ slope of the other line=m2} \\ The\text{ angle betw}en\text{ two line is 60} \\ \tan 60=|\frac{m1-m2}{1+m1m2}| \\ \sqrt{3}\text{ =|}\frac{2-m2}{1+3m2}| \\ \sqrt{3}\text{ =}\pm\frac{2-m2}{1+3m2} \\ \sqrt{3}=\mleft\lbrace\frac{2-m2}{1+3m2}\text{ }\mright\rbrace\text{or }\sqrt{\text{ 3}}\text{ =-}\mleft\lbrace\frac{2-m2}{1+3m2}\mright\rbrace \\ \sqrt{3}(1+3m2)=(2-m2)\text{ or}\sqrt{\text{ 3}}(1+3m2)\text{ =-(2-m2)} \\ \sqrt{3}+3\sqrt{3}m2+m2=2\text{ or }\sqrt[]{3}+3\sqrt[]{3}m2-m2=-2 \\ m2=\frac{(2-\sqrt[]{3})}{(2\sqrt{3}+1)}\text{ or m2=-}\frac{(2-\sqrt[]{3})}{(2\sqrt[]{3}+1)} \\ The\text{ equation of line passing through (2,3) and having slope }\frac{(2-\sqrt[]{3})}{(2\sqrt[]{3}+1)} \\ y-3=\frac{(2-\sqrt[]{3})}{(2\sqrt[]{3}+1)}(x-2) \\ y(2\sqrt{3}+1)-3(2\sqrt{3}+1)=(2-\sqrt{3})x-2(2-\sqrt{3}) \\ (\sqrt{3}-2)x+(2\sqrt[]{3}+1)y=-1+8\sqrt[]{3} \\ \text{THis is the equation of other line.} \end{gathered}[/tex]
