org.json.JSONObject constructor not accepting what appears to be a valid JSON string
You are trying to create a JSONObject, but what you are actually giving it is a JSONArray. Did you try creating a JSONArray instead?
Alternatively, you could wrap your array in an object so that you can create a JSONObject out of it.
I would suggest using the GSon library instead as it appears to be more full-featured.
In addition, it may be helpful to use this tool to test your data (your data is valid btw):