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How to find out value of product

$$\cos{\theta}\cos{2\theta}\cos{3\theta}...\cos{999\theta}$$ where

$\theta=\frac{2\pi}{1999}$

i tried to multiply and divide by sin\theta to convert to sin2A, but couldnot do it. i would like to know many methods, if possible, to do this question

thanks

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    Well, whatever it is, it must be EXTREMELY close to zero. – 2017-02-09
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    @Rohan How do you find duplicates so fast? – 2017-02-09
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    @S.C.B Fast?? I found it 14 minutes after the OP posted the question. Just search the site, sir. – 2017-02-09
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    @Rohan I couldn't find it when I searched the site. – 2017-02-09
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    @S.C.B Sir, put this in the search box: `Find the value of $\cos x \cos 2x ` – 2017-02-09
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    @Rohan How do you know to put that? I put in `$\cos{\theta}\cos{2\theta}\cos{3\theta}...\cos{999\theta}$` – 2017-02-09
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    @dxiv odd angles are left out – 2017-02-09
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    @TaylorTed I spoke too hastily, thanks for the correction. – 2017-02-09

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