1. **State the problem:** Given $\cos \theta = \frac{2}{3}$, find $\sec \theta$ using the reciprocal identity. 2. **Recall the reciprocal identity:** $$\sec \theta = \frac{1}{\cos \theta}$$ 3. **Substitute the given value:** $$\sec \theta = \frac{1}{\frac{2}{3}}$$ 4. **Simplify the fraction:** $$\sec \theta = \frac{1}{\frac{2}{3}} = \frac{1 \times 3}{2} = \frac{3}{2}$$ 5. **Rationalize the denominator if needed:** Here, the denominator is already rational, so no further steps are needed. **Final answer:** $$\sec \theta = \frac{3}{2}$$