I wouldn't do two short rods. I think those always look a little odd, but that's just my thoughts. If it were my room, I'd find a rod with a very small bracket. I'd install the bracket so when hung, the top edge of the drapes was even with the bottom of the crown. You will need to put your bracket on the crown unfortunately. I'd do 1 rod that extended 18-24 inches beyond the window so only the side window trim is covered by the drape. Unfortunately, your crown is getting in the way of hanging a rod! But, if you get the right bracket/rod I think it will work out nice. My only other suggestion is to do a roman or balloon shade in a fabric pattern and let the crown be the picture frame around your window. It is very lovely on it own.

I used the type of rings that annz linked to, and also just removed the clips. (This is because I am cheap, and already had them on hand, LOL). They also sell the rings with just the little metal loops. If you're planning to put the pins into loops (rather than hooking the pins directly onto a traverse rod or something), it's better to use the pins that are triangular at the top - it will keep them from sliding forward/backward. The pins do work better if the header of the drape has some "stiffness" to it, that's a good point. Look at the drapes you're trying to hang, it should be pretty obvious. You can hang them even if there isn't a lining/backer, but they may look a little saggy. (Serious sewing people look away: If you want to add some stiffness, you can buy iron-on interfacing at the craft store. Cut pieces to the height of your header, and iron them on the back of the drape. For a step above that, unpick the seam, iron the interfacing on the inside, and re-sew. If you ever change your mind, you can re-iron the interfacing and remove while it's still hot.) The closer together you put the pins/rings, the more "folds" you'll have in your fabric when the drapes are open. Fewer pins/rings means that there will be more fabric to stick out from the wall when the drapes are open, and the possibility of sagging between rings. I don't think there's a "wrong" way - whatever looks best to you. With a pre-pleated panel, you're obligated to put one at each pleat; a flat panel lets you adjust it to your liking. Personally, I like having an odd number of hanging points. For the panels in the picture above, I put 7 on each panel. Since they were about 52" wide, that meant there was a ring on each end, then spaced about 8-9" between. It probably could have used 9 per panel, but I only had 14 total (see above w/r/t cheap and lazy) :-D To space them, I installed the pins in this way (no measuring tape required!). Put one in each end, about 1-2" from the actual end. Fold panel in half, width-wise, and place a pin at the center fold. On the right side (defined as "between the center pin and the right edge pin"), fold the panel into 1/3s so you'll end up with two folds - like you do a letter; place a pin at each fold. Repeat this on the left side. This will give you 7, reasonably-even spaced pins, with no measuring. To do 9 pins, you would fold each side into 1/4s - i.e. in half twice - to give you two edge pins, one center pin, and three on each side. ... I can't believe I've just written an entire novella about drapery pins. LOL

Thanks everyone for the suggestions about my arched window. I’m considering them. Previous owners had a straight double rod with the drapery hanging from them for all windows, including arched window and it did cover up the beautiful window and the shelving on the sides. While I’m deciding on the arched window treatment, This room has 3 other windows as well that are not arched. I’m thinking about how to match all the window treatments in this room. It was mentioned to not use grommet since it is modern. What would you suggest for this type of room? Maybe euro-pleated. I definitely want to use a double rod for privacy purposes. I’m in the process of looking at different stores to buy a few drapes and try them out and see how it looks.

The pic is so small I can't see the details. Are you asking about the panels and the sheers or just the panels? From what I can see, the panels look like they're hangling from rings, but impossible to see what kind of pleats were used. They're definitely not grommets. Can't tell about the sheers at all.