Sum, Difference, and Multiple-Angle Formulas · Challenge problem

Two sinusoidal waves $y_1=\sin(\omega t)$ and $y_2=\sin(\omega t+\varphi)$, with $0<\varphi<\pi$, are added together. Suppose the sum is $y_1+y_2=\sqrt3\sin\!\left(\omega t+\dfrac{\pi}{6}\right)$ for every value of $t$. Find $\varphi$.