The product of \[\cos \theta \cos 2\theta \cos 3\theta ...\cos ({{2}^{n-1}}\theta )\]is

• A. \[\frac{\sin ({{2}^{n}}\theta )}{{{2}^{n}}\sin \theta }\]
• B. \[\frac{cos({{2}^{n}}\theta )}{{{2}^{n}}\cos \theta }\]
• C. \[\frac{cosn\theta }{{{2}^{n}}\cos \theta }\]
• D. \[\frac{sin({{2}^{n}}\theta )}{\sin \theta }\]