$$(1+ \cos \frac{ \pi }{ 8 } )(1+ \cos \frac{ 3 }{ 8 } \pi )(1+ \cos \frac{ 5 }{ 8 } \pi )(1+ \cos \frac{ 7 }{ 8 } \pi )$$
$\frac{\sqrt{2}}{4}-\frac{\sqrt{2}}{4}+\frac{1}{8}\approx 0.125$
