\(4 - \frac{1}{2 - \sqrt{3}} = \frac{4(2 - \sqrt{3}) - 1}{2 - \sqrt{3}}\)

= \(\frac{8 - 4\sqrt{3} - 1}{2 - \sqrt{3}}\)

= \(\frac{7 - 4\sqrt{3}}{2 - \sqrt{3}}\)

Rationalizing,

\((\frac{7 - 4\sqrt{3}}{2 - \sqrt{3}}) (\frac{2 + \sqrt{3}}{2 + \sqrt{3}})\)

= \(\frac{14 + 7\sqrt{3} - 8\sqrt{3} - 12}{4 + 2\sqrt{3} - 2\sqrt{3} - 3}\)

= \(\frac{2 - \sqrt{3}}{1} = 2 - \sqrt{3}\)