What is the value of \(\cos \left( {\frac{{{\rm{A}} + {\rm{B}}}}{2}} \right)\cos \left( {\frac{{{\rm{B}} + {\rm{C}}}}{2}} \right)\cos \left( {\frac{{{\rm{C}} + {\rm{A}}}}{2}} \right)?\)

• A. \(\frac{1}{4}\)
• B. \(\frac{1}{2}\)
• C. \(\frac{1}{{16}}\)
• D. None of the above