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Prove that cos(2pi)/(15)cos(4pi)/(15)cos...

Prove that `cos(2pi)/(15)cos(4pi)/(15)cos(8pi)/(15)cos(14pi)/(15)=1/(16)`

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Here, we will use,
`2sinxcosx = sin2x`
Now,
`L.H.S. = 16cos((2pi)/15)cos((4pi)/15)cos((8pi)/15)cos((16pi)/15)`
`=16cos((2pi)/15)cos((4pi)/15)cos((8pi)/15)cos(pi+pi/15)`
`=16cos((2pi)/15)cos((4pi)/15)cos((8pi)/15)(-cos(pi/15))`
`=-16cos(pi/15)cos((2pi)/15)cos((4pi)/15)cos((8pi)/15)`
`=8/sin(pi/15)*2sin(pi/15)cos(pi/15)cos((2pi)/15)cos((4pi)/15)cos((8pi)/15)`
...
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