Evaluate $ cos a cos 2 a cos 3 a cdots cos 999 a $ where $a=frac{2 pi}{1999}$

Evaluate
$
cos a cos 2 a cos 3 a cdots cos 999 a
$
where $a=frac{2 pi}{1999}$

I know this question has already been answered many times but my doubt is different

Solution: Let $P$ denote the desired product, and let

$
Q=sin a sin 2 a sin 3 a cdots sin 999 a
$

Then
$
begin{aligned}
2^{999} P Q=&(2 sin a cos a)(2 sin 2 a cos 2 a) cdots(2 sin 999 a cos 999 a) \
=& sin 2 a sin 4 a cdots sin 1998 a \
=&(sin 2 a sin 4 a cdots sin 998 a)[-sin (2 pi-1000 a)] \
& cdot[-sin (2 pi-1002 a)] cdots[-sin (2 pi-1998 a)] \
=& (sin 2 a sin 4 a cdots sin 998 a) sin 999 a sin 997 a cdots sin a=Q
end{aligned}
$

how they got this last step from previous one ???