Chapter 7 - Analytic Trigonometry - 7.6 Double-angle and Half-angle Formulas - 7.6 Assess Your Understanding - Page 498: 67

See below.

$LHS=tan(2\theta+\theta)=\frac{tan(2\theta)+tan\theta}{1-tan(2\theta)tan\theta}=\frac{\frac{2tan\theta}{1-tan^2\theta}+tan\theta}{1-(\frac{2tan\theta}{1-tan^2\theta})tan\theta}=\frac{2tan\theta+tan\theta-tan^3\theta}{1-tan^2\theta-2tan^2\theta}=\frac{3tan\theta-tan^3\theta}{1-3tan^2\theta}=RHS$