trigonometry - Solving $sin 7phi+cos 3phi=0$

The question is find the general solution of this equation:

$$\sin(7\phi)+\cos(3\phi)=0$$

I tried to use the "Sum-to-Product" formula, but found it only suitable for $\sin(a)\pm \sin(b)$ or $\cos(a)\pm \cos(b)$. So I tried to expand $\sin 7\phi$ and $\cos 3\phi$, but the equation became much more complicated..

I'm self studying BUT There's nothing about how to solve this type of equations on my textbook..

reeeaaaaally confused now..

Answer

Hint: Use sum to product!

$$\sin 7\phi+\sin \left(\frac{\pi}{2}-3\phi \right)=0$$