The value of \( \sin 10^\circ \sin 50^\circ \sin 70^\circ \): \[ = \frac{\sin(3 \times 10^\circ)}{4} = \frac{1}{8} \] (using \( \sin \theta \sin (60^\circ - \theta) \sin (60^\circ + \theta) = \frac{\sin 3\theta}{4} \))