Hello,

Let N be this sum.

If you replace the sinus with cosine, you'll get something interesting :

So replace for each term.

You'll have :

But we know that

So if we replace again :

(1)

The aim will be to retrieve N in the brackets. So tihere is missing and an extra .

sin(0)=0, so we can remove . As sin(90°)=1,

By using (1) :

And then you have N