Find exact values using identities

It is given that \(\cos 15° = \frac{1}{2}\sqrt{2 + \sqrt{3}}\) and \(\sin 15° = \frac{1}{2}\sqrt{2 - \sqrt{3}}\) Show that \(\tan^2 15°\) can be written in the form \(a + b\sqrt{3}\), where \(a\) and \(b\) are integers. Fully justify your answer. [3 marks]