How to find the value of this trigonometric expression

Question

I am new to trigonometry. I need to evaluate the below expression:

$$ 96\sqrt{3} \ \sin\left(\frac \pi {48}\right) \cos\left(\frac \pi {48}\right) \cos\left(\frac \pi{24}\right)\cos\left(\frac \pi {12}\right) \cos\left(\frac \pi 6\right) $$

I need to use basic identities, such as double angle formulae, Trigonometric ratios

Answer 1

$$ 96\sin(\pi/48)\cos(\pi/48) = 48 \times \underbrace{2\sin\left(\frac \pi {48} \right) \cos\left( \frac \pi{48}\right)} = 48 \underbrace{\sin\left( 2\times\frac \pi{48} \right)} $$ by the usual double-angle formula, and then $$ = 48\sin \left( \frac \pi {24}\right). $$ Next, do the same thing with $24$ that we just did with $48,$ then with $12,$ then with $6.$