Given:

A line which is passing through \( (2, 2\sqrt{3})\), the angle is 75°

By using the formula,

The equation of line is [y – y_{1} = m(x – x_{1})]

Here, angle, θ = 75°

The slope of the line, m = tan θ

m = tan 75°

= 3.73 = \( 2 + \sqrt{3}\)

The line passing through (x_{1}, y_{1}) =\( (2, 2\sqrt{3})\)

The required equation of the line is y – y_{1} = m(x – x_{1})

Now, substitute the values, we get

\( y – 2\sqrt{3} = 2 + \sqrt{3} (x – 2)\)

\( y – 2\sqrt{3} = (2 + \sqrt{3})x – 7.46\)

\( (2 + \sqrt{3})x – y – 4 = 0\)

The equation of the line is \( (2 + \sqrt{3})x – y – 4 = 0\)

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