Without using a calculator,
Show that \(\sin15^\circ=\dfrac{\sqrt6-\sqrt2}{4}\).[2]
Given that \(\cos15^\circ=\dfrac{\sqrt6+\sqrt2}{4}\), find the exact value of \(\dfrac{\sin15^\circ+\cos15^\circ}{2-\sqrt3}\). Give your answer in the form \(a\sqrt6+b\sqrt2\), where \(a\) and \(b\) are rational numbers.[4]
Explain, without the use of a calculator, why your answer is greater than 3.[1]