What is the value of \(\left( {1 + \cos \frac{{\rm{\pi }}}{8}} \right)\left( {1 + \cos \frac{{3{\rm{\pi }}}}{8}} \right)\left( {1 + \cos \frac{{5{\rm{\pi }}}}{8}} \right)\left( {1 + \cos \frac{{7{\rm{\pi }}}}{8}} \right)?\)

• A. \(\frac{1}{2}\)
• B. \(\frac{1}{2} + \frac{1}{{2\sqrt 2 }}\)
• C. \(\frac{1}{2} - \frac{1}{{2\sqrt 2 }}\)
• D. \(\frac{1}{8}\)