docs: Add LiteLLM self-hosted proxy documentation

Added documentation for setting up and using LiteLLM as a self-hosted proxy server with Roo Code. Includes configuration examples for multiple providers (Anthropic, OpenAI, Azure).

Author: colesmcintosh

docs/getting-started/connecting-api-provider.md

@@ -29,6 +29,49 @@ LLM routers let you access multiple AI models with one API key, simplifying cost
 
 *OpenRouter dashboard with "Create key" button. Name your key and copy it after creation.*
 
+#### LiteLLM
+
+[LiteLLM](https://litellm.ai/) is an open-source LLM gateway that provides access to 100+ AI models through a unified OpenAI-compatible API. Set up a self-hosted proxy server to route requests to multiple providers through a single endpoint.
+
+1. Install LiteLLM: `pip install 'litellm[proxy]'`
+
+2. Create a configuration file (`config.yaml`) to define your models:
+   ```yaml
+   model_list:
+     # Configure multiple Anthropic models
+     - model_name: claude-3-7-sonnet
+       litellm_params:
+         model: anthropic/claude-3-7-sonnet-20250219
+         api_key: os.environ/ANTHROPIC_API_KEY
+     
+     # Configure OpenAI models
+     - model_name: gpt-4o
+       litellm_params:
+         model: openai/gpt-4o
+         api_key: os.environ/OPENAI_API_KEY
+     
+     # Configure Azure OpenAI
+     - model_name: azure-gpt-4
+       litellm_params:
+         model: azure/my-deployment-name
+         api_base: https://your-resource.openai.azure.com/
+         api_version: "2023-05-15"
+         api_key: os.environ/AZURE_API_KEY
+   ```
+
+3. Start the LiteLLM proxy server:
+   ```bash
+   # Using configuration file (recommended)
+   litellm --config config.yaml
+   
+   # Or quick start with a single model
+   export ANTHROPIC_API_KEY=your-anthropic-key
+   litellm --model claude-3-7-sonnet-20250219
+   ```
+
+4. The proxy will run at `http://0.0.0.0:4000` by default
+
+
 #### Requesty
 
 1. Go to [requesty.ai](https://requesty.ai/)
@@ -78,6 +121,11 @@ Once you have your API key:
 4. Select your model:
    - For **OpenRouter**: select `anthropic/claude-3.7-sonnet` ([model details](https://openrouter.ai/anthropic/claude-3.7-sonnet))
    - For **Anthropic**: select `claude-3-7-sonnet-20250219` ([model details](https://www.anthropic.com/pricing#anthropic-api))
+   - For **LiteLLM**: 
+     - Set the API provider to "OpenAI Compatible"
+     - Enter your proxy URL (e.g., `http://localhost:4000`)
+     - Use any string as the API key (e.g., "sk-1234")
+     - Select the model name you configured in your `config.yaml`
 
 :::info Model Selection Advice
 We strongly recommend **Claude 3.7 Sonnet** for the best experience—it generally "just works" out of the box. Roo Code has been extensively optimized for this model's capabilities and instruction-following behavior.