\(\cos 165 = -\cos (180 - 165) = -\cos 15\)

\(\cos 15 = \cos (45 - 30)\)

\(\cos (x - y) = \cos x \cos y + \sin x \sin y\)

\(\cos (45 - 30) = \cos 45 \cos 30 + \sin 45 \sin 30\)

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

= \(\frac{1}{4}(\sqrt{6} + \sqrt{2})\)

\(\therefore \cos 165 = -\frac{1}{4}(\sqrt{6} + \sqrt{2})\)