Phishing remains a critical cybersecurity threat, increasingly leveraging psychological manipulation and obfuscation to evade traditional detection. This study investigates whether DeepSeek-R1, the advanced large language model (LLM) currently open source, can be fine-tuned to be an effective solution for phishing email detection. Using public datasets from Hugging Face, the model was fine-tuned via the Unsloth framework and tested on both standard and obfuscated phishing samples. The model achieved an accuracy of 83.3%, a precision of 85%, and a recall of 80%, indicating good overall performance. It detected 89% of text-obfuscated and 96% of URL-obfuscated phishing emails, suggesting robust semantic understanding beyond keyword matching. However, challenges remain in minimizing false negatives and adapting to complex spear-phishing scenarios. This case study demonstrates the potential of fine-tuned LLMs for text-based phishing detection and highlights directions for future research in adversarial robustness and multimodal detection integration.