Simplify \(\cos{\pi }\) to \(-1\).
\[(1+\frac{-1}{8})(1+\frac{\cos{3}}{8}\pi )(1+\frac{\cos{5}}{8}\pi )(1+\frac{\cos{7}}{8}\pi )=\frac{1}{8}\]
Move the negative sign to the left.
\[(1-\frac{1}{8})(1+\frac{\cos{3}}{8}\pi )(1+\frac{\cos{5}}{8}\pi )(1+\frac{\cos{7}}{8}\pi )=\frac{1}{8}\]
Simplify \(1-\frac{1}{8}\) to \(\frac{7}{8}\).
\[\frac{7}{8}(1+\frac{\cos{3}}{8}\pi )(1+\frac{\cos{5}}{8}\pi )(1+\frac{\cos{7}}{8}\pi )=\frac{1}{8}\]
Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
\[\frac{7}{8}(1+\frac{\cos{3}\pi }{8})(1+\frac{\cos{5}}{8}\pi )(1+\frac{\cos{7}}{8}\pi )=\frac{1}{8}\]
Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
\[\frac{7}{8}(1+\frac{\cos{3}\pi }{8})(1+\frac{\cos{5}\pi }{8})(1+\frac{\cos{7}}{8}\pi )=\frac{1}{8}\]
Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
\[\frac{7}{8}(1+\frac{\cos{3}\pi }{8})(1+\frac{\cos{5}\pi }{8})(1+\frac{\cos{7}\pi }{8})=\frac{1}{8}\]
Since \(\frac{7}{8}(1+\frac{\cos{3}\pi }{8})(1+\frac{\cos{5}\pi }{8})(1+\frac{\cos{7}\pi }{8})=\frac{1}{8}\) is false, there is no solution.
[No Solution]
