Remove Double Linebreaks In String?

I am developing a asp.net web application, i have a string (with a value in it from a database), with multiple lines that i put in a TextBox with mulitline type. (textarea)

Now the problem is, that in the string are multiple lines, with much empty space. so i want the remove only the double linebreaks.

example of my textbox:

{empty}
{empty}
'This is some text in the textbox on line 3
'some text on line 4
{empty}
'some text on line 6
{empty}
{empty}
'some text on line 9
{empty}

now somehow i want to remove line 1 and 2, and line 7 and 8