Now, \( \Large \sin 12 ^{\circ} \sin 48 ^{\circ} \sin 54 ^{\circ} \)

 \( \Large =  \frac{1}{2} \left(\cos 36 ^{\circ} -\cos 60 ^{\circ} \right) \cos 36 ^{\circ} \)

= \( \Large \frac{1}{2}\left[ \frac{\sqrt{5}+1}{4}-\frac{1}{2} \right]\left[ \frac{\sqrt{5}+1}{4} \right]=\frac{5-1}{32}=\frac{4}{32}=\frac{1}{8} \)