I would like to calculate:
$$ \prod_{x=1}^{44}\left(1-\frac{1}{\tan(x°)}\right) $$
Here is what I found:
$$ 1-\frac{1}{\tan(x)}=\frac{\sqrt{2}\sin(x-45°)}{\sin(x)} $$
$$ \prod_{x=1}^{44}\left(1-\frac{1}{\tan(x°)}\right)=\prod_{x=1}^{44} \frac{\sqrt{2}\sin(x-45°)}{\sin(x)}=2^{22} \frac{\prod_{x=1}^{44} \sin(x-45°)}{\prod_{x=1}^{44} \sin(x)} $$
$$ x\rightarrow 45°-x $$
$$ \prod_{x=1}^{44}\left(1-\frac{1}{\tan(x°)}\right)=\frac{\prod_{x=1}^{44} -\sin(x)}{\prod_{x=1}^{44} \sin(x)}=2^{22} $$