# Trigo Lovers cannot be short of problems

**Geometry**Level 4

\[\large \left( \frac12 + \cos\left(\frac\pi{20}\right)\right) \left( \frac12 + \cos\left(\frac{3\pi}{20}\right)\right) \left( \frac12 + \cos\left(\frac{9\pi}{20}\right)\right) \left( \frac12 + \cos\left(\frac{27\pi}{20}\right)\right) = \ ? \]

Give your answer to 4 decimal places.