Write down the value of $\sin \theta$ .

Find the value of $\tan 2\theta$ .

Find the value of $\cos \left( {\frac{\theta }{2}} \right)$ , giving your answer in the form $\frac{{\sqrt a }}{b}$ where a , $b \in {\mathbb{Z}^ + }$ .

$\sin \theta = \frac{{\sqrt 8 }}{3}$     A1

[1 mark]

$\tan 2\theta = \frac{{2 \times \sqrt 8 }}{{1 - 8}} = - \frac{{2\sqrt 8 }}{7}\,\,\,\,\,\left( { - \frac{{4\sqrt 2 }}{7}} \right)$     M1A1

[2 marks]

${\cos ^2}\left( {\frac{\theta }{2}} \right) = \frac{{1 + \frac{1}{3}}}{2} = \frac{2}{3}$     M1A1

$\cos \left( {\frac{\theta }{2}} \right) = \frac{{\sqrt 6 }}{3}$     A1

[3 marks]