Combine tan⁻¹2/3 + tan⁻¹1/5 and tan⁻¹2/3 - tan⁻¹1/5 into single inverse tangents and give their…

Step 1. The sum. $xy = \dfrac{2}{15} < 1$. The fraction is $\dfrac{\frac{2}{3} + \frac{1}{5}}{1 - \frac{2}{15}} = \dfrac{13/15}{13/15} = 1$. So the sum is $\tan^{-1}1 = \dfrac{\pi}{4} = 0.7854$.

Step 2. The difference. The fraction is $\dfrac{\frac{2}{3} - \frac{1}{5}}{1 + \frac{2}{15}} = \dfrac{7/15}{17/15} = \dfrac{7}{17}$. So the difference is $\tan^{-1}\dfrac{7}{17} = 0.3906$.