The philosophy of Chapter 4 is that you must have attainment through the practice of karma yoga. In the context of karma yoga, it has also given practical psychological techniques to help overcome the fluctuating mind by becoming free of raga, attraction or attachment, bhaya, fear, and krodha, anger.
Chapter 4 also says that jnana, the aspect of wisdom or applied knowledge, and karma, action, have to merge together so that jnana becomes active and alive, and karma becomes free from the bondage of sattwa, rajas and tamas. This gives freedom from both sides; freedom as you are living in wisdom and freedom as actions are not creating any further karmas along the way.
Sannyasa represents the aspect of renunciation and one of the prerequisites of sannyasa is that you have to renounce expectations and attachments. The entire gist of chapter 4 is found in this sloka:
Therefore, Arjuna, cutting asunder with the sword of knowledge this doubt in your heart born of ignorance, establish yourself in karma yoga and stand up for the fight. (4:42)
Taking up the sword is an action, a karma, but the form of the sword is wisdom. So karma and jnana have combined together and you are, through sannyasa, cutting yourself off from the doubting nature. That is sannyasa. If you truly ask yourself what is the ultimate aim of sannyasa, you realize it is the elimination of the doubting nature.