This expression can be evaluated by applying the triple angle formula (see %%HREF%%2255%%) twice: \begin{align*} &\cos 6^\circ\cos 42^\circ \cos 66^\circ\cos 78^\circ\\ =\quad&\cos 6^\circ\cos 42^\circ \cos 66^\circ\cos 78^\circ\cdot\frac{\cos 54^\circ}{\cos 54^\circ}\\ =\quad&(\cos 6^\circ\cos 54^\circ\cos 66^\circ)\cdot\frac{ \cos 42^\circ \cos 78^\circ}{\cos 54^\circ}\\ =\quad&(\cos 6^\circ\cos (60^\circ-6^\circ)\cos (60^\circ+6^\circ))\cdot\frac{ \cos 42^\circ \cos 78^\circ}{\cos 54^\circ}\\ =\quad&\frac{\cos (3\cdot 6^\circ)}{4}\cdot\frac{ \cos 42^\circ \cos 78^\circ}{\cos 54^\circ}\\ =\quad&\frac{1}{4}\cdot\frac{1}{\cos 54^\circ}\cdot \cos 18^\circ \cos 42^\circ \cos 78^\circ\\ =\quad&\frac{1}{4}\cdot\frac{1}{\cos 54^\circ}\cdot\frac{1}{4}\cdot \cos (3\cdot 18^\circ)\\ =\quad&\boxed{\frac{1}{16}} \end{align*}