How can we accurately recommend unpopular items and increase their exposure to users? Previous models fail to handle the skewed distribution of item interactions, resulting in an overemphasis on popular items and inadequate recommendations of unpopular tail items. Existing approaches that address this imbalance often sacrifice overall accuracy to boost the accuracy of recommending tail items, or overlook the limited presence of tail items in the recommendations. In this paper, we propose DART (Diversified and AccuRate Long-Tail Recommendation), an accurate and diversified recommendation method which evenly recommends items across all popularity groups while maintaining high accuracy within each group. We increase the interactions of tail items by generating synthetic sequences which preserve original user preferences. DART improves the representation of tail items through contrastive learning which facilitates the learning of the relationships between similar head and tail items. Additionally, we ensure that only reliable information is learned in the embedding of tail items through a popularity-based negative sampling. Experimental results demonstrate that DART achieves up to 44.7% higher Coverage@10 and 47.5% higher nDCG@10 for tail items as ground-truth compared to the best competitor while improving the overall nDCG@10 by up to 22%.