KöMaL 2010 B4250

The centre of the regular hexagon ABCDEF in the coordinate plane is at the origin $O$, and vertex $A$ is the point (0,1). Let $\mathcal{H}_1$ and $\mathcal{H}_2$ denote the set of points inside or on the boundary of the regular triangles ACE and BDF , respectively. Determine the set of points $P$ for which the vector $\overrightarrow{OP}$ can be written in the form $\overrightarrow{OP_1}+\overrightarrow{OP_2}$, where $P_1\in \mathcal{H}_1$ and $P_2\in \mathcal{H}_2$.