Chapter 7 - Trigonometric Identities and Equations - 7.3 Sum and Difference Identities - 7.3 Exercises - Page 679: 36

$$\theta = {20^ \circ }$$

$$\eqalign{ & \sin \theta = \cos \left( {2\theta + {{30}^ \circ }} \right) \cr & {\text{Use the cofunction identity }}\sin \theta = \cos \left( {{{90}^ \circ } - \theta } \right),{\text{ then}} \cr & {90^ \circ } - \theta = 2\theta + {30^ \circ } \cr & {\text{Solving for }}\theta \cr & {90^ \circ } - {30^ \circ } = 2\theta + \theta \cr & 3\theta = {60^ \circ } \cr & \theta = {20^ \circ } \cr} $$