How about white vertical blinds that draw from the outer edges to the meeting point.

Not a fan of vertical. Why cover them? Very pretty view. Why not frame them in white moulding 3". Then hang simple light weight fabric panels on each end. A print, with some of wall color in them.

I would remove verticals from slider to. Do same as suggested on other window. Then put same panels on all window. You don't. Have to frame out.

I am sure how expensive an L shaped drapery rod is. Try purchasing one or two drapery panels wide enough to cover both windows. A coordinating drapery could be used in the next room (one with vertical blinds). Verticals can be expensive. At least with the drapes, you could take those with you

it's a bit unconventional, but check out this picture where they used elbow brackets for windows such as yours: [houzz=]

Ikea has corner rods that are easy on the budget. Umbra also has a bay window rod, that should work for your space. For the Umbra, its sold as a one set. Leave off the left rod, and use the middle rod, right rod and finials.

Take down the verticals on the adjacent slider. Purchase rods for both that can extend past the frame as much as seems right, and then buy grommet topped curtains. Buy four panels for the slider and two for the long side of the aquarium - when you hang them, overlap the grommets inside each other for the double paneled side - a sheer pretty linen weave would give you privacy and filter direct sunlight but keep your green view.

Leaded glass windows suspended in the space. www.isaacdsmith.com

Also, Target has some really cute matchstick blinds & roman shades which are very affordable.

Since you're renting, check with the landlord before you toss his verticals. May need to save them in the attic/basement & reinstall before you move out to get your deposit back!

Didn't know you were renting. Bamboo easy to put up and remove.

Your solution will depend on what kind of coverage you need. Do you want cafe style curtains to let light in but still maintain some privacy? Also, do you need complete black out coverage, or do you prefer a sheer curtain or panel? Some things to consider: the proximity of your neighbors or foot traffic, what the room is used for and natural light currently in there, etc. Otherwise I think you have a good bunch of suggestions above. Personally I would go with the L-shaped curtain rod

You may need this if you are considering curtain rods

Interesting post.

I think Roman Shades would give the room a sophisticated look while giving you privacy and shade when needed. Go with a natural color to pair with the vibrant wall color you have now. Check out our website for more products here: http://www.blindsgalore.com/WindowProduct.asp?id=749840

Best of luck!
Blindsgalore Team