Does $\alpha\leq \beta+ \gamma$ imply $\sin \alpha \leq \sin \beta+\sin\gamma$?

Here is the question: Suppose that $\alpha,\beta,\gamma\in [0,\frac{\pi}{2}]$ and $\alpha\leq \beta + \gamma$. Is it true that $\sin \alpha \leq \sin \beta+\sin\gamma$? I do not really know how to solve this one. I would be grateful for any hints.