Given:

A line which is passing through \[(2,\text{ }2\surd 3),\text{ }the\text{ }angle\text{ }is\text{ }{{75}^{o}}\]

By using the formula,

The equation of line is \[[y\text{ }-\text{ }{{y}_{1}}~=\text{ }m(x\text{ }-\text{ }{{x}_{1}})]\]

Here, angle, \[\theta \text{ }=\text{ }{{75}^{o}}\]

The slope of the line, \[m\text{ }=\text{ }tan\text{ }\theta \]

\[m\text{ }=\text{ }tan\text{ }{{75}^{o}}\]

\[=\text{ }3.73\text{ }=\text{ }2\text{ }+~\surd 3\]

The line passing through \[({{x}_{1}},\text{ }{{y}_{1}})\text{ }=~(2,\text{ }2\surd 3)\]

The required equation of the line is \[y\text{ }-\text{ }{{y}_{1}}~=\text{ }m(x\text{ }-\text{ }{{x}_{1}})\]

Now, substitute the values, we get

\[y\text{ }-2\surd 3~=\text{ }2\text{ }+~\surd 3~\left( x\text{ }-\text{ }2 \right)\]

\[y\text{ }-\text{ }2\surd 3\text{ }=\text{ }(2\text{ }+~\surd 3)x – 7.46\]

So,

\[(2\text{ }+~\surd 3)x – y – 4\text{ }=\text{ }0\]

∴ The equation of the line is \[(2\text{ }+~\surd 3)x – y -4\text{ }=\text{ }0\]