Trigonometry (10th Edition)

$\theta=2^{\circ}$
1. Tangent and cotangent are reciprocals $\tan\theta=\frac{1}{\cot 5\theta}$ 2. Rewrite cotangent as a tengent $\tan(3\theta -4^{\circ})=\tan(5\theta-8^{\circ})$ 3.Since the tangent values are equal, the angles themselves must be equal. $5\theta -3\theta= -4+8$ $2\theta=4$ $\theta=2^{\circ}$