🧠 Backend: Syllabus Generation & Course Planning

## Phase 1: MVP Core Logic

Implement the conversational syllabus generator and course planning logic.

### Tasks
- [ ] Implement Pydantic Models for Course, Topic, Video
- [ ] Build GeminiService for Syllabus Generation (Prompt Engineering)
- [ ] Create API Endpoint: POST /generate-syllabus
- [ ] Design prompt templates for course negotiation
- [ ] Implement structured output parsing from Gemini responses

### Acceptance Criteria
- User can chat to define learning goals, target audience, difficulty
- System generates structured Topics and Subtopics with learning outcomes
- API returns valid JSON following Pydantic schema
- Error handling for malformed Gemini responses

### Tech Stack
- FastAPI
- Pydantic V2
- Google Gemini API
- Structured output prompting