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Geometry Level 3

If the value of

(1+cosπ8)(1+cos3π8)(1+cos5π8)(1+cos7π8)\left( 1\quad +\quad cos\frac { \pi }{ 8 } \right) \left( 1\quad +\quad cos\frac { 3\pi }{ 8 } \right) \left( 1\quad +\quad cos\frac { 5\pi }{ 8 } \right) \left( 1\quad +\quad cos\frac { 7\pi }{ 8 } \right)

can be written as xy\frac { x }{ y }, then find out the value of x + y.

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