- Without using tables, show for \(\theta=15^\circ\) that \(\sin\theta=\dfrac{\sqrt{6}-\sqrt{2}}{4}\), and find the values of \(\cos\theta\) and \(\tan\theta\).

For what angles do we know the exact values of \(\sin\theta\)?

What trigonometric formulae might be useful here? How about expanding \(\sin(a-b)\), choosing \(a\) and \(b\) carefully?