Don't try to multiply!

Geometry Level 4

(1+cosπ9)(1+cos3π9)(1+cos5π9)(1+cos7π9)\left( 1+\cos { \frac { \pi }{ 9 } } \right) \left( 1+\cos { \frac { 3\pi }{ 9 } } \right) \left( 1+\cos { \frac { 5\pi }{ 9 } } \right) \left( 1+\cos { \frac { 7\pi }{ 9 } } \right)

The value of the expression above can be expressed as PQ \dfrac PQ, where PP and QQ are coprime positive integers, find QPQ-P .

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