$\begin{aligned} \text { Given } \sin \theta &=\sin 15^{\circ}+\sin 45^{\circ} \\ &=2 \sin \left(\frac{15^{\circ}+45^{\circ}}{2}\right) \cos \left(\frac{15^{\circ}-45^{\circ}}{2}\right) \\ &=2 \sin 30^{\circ} \cos 15^{\circ}=2 \times \frac{1}{2} \cos 15^{\circ} \\ \sin \theta &=\cos 15^{\circ} \Rightarrow \sin \theta=\sin \left(90^{\circ}-15^{\circ}\right) \Rightarrow \theta=75^{\circ} \end{aligned}$