Trigonometry

We are taking the product of $cos 1\times cos2\times cos 3....\times cos 2016$ . We know that there is some value whose $cos =0$ $\implies$ , the product=0. ( for example $cos 90=0$ )

$\cos{90}^°$ comes in between which is $0$ making the entire product $\color{#3D99F6}{\boxed{0}}$ .

$cos1\times cos2\times cos3\times...\times cos2016=cos1\times cos2\times...\times cos90\times...\times cos2016 = cos1\times cos2\times ... \times 0 \times ... \times cos2016 = 0$