As shown in the figure, a point $P_{0}$ moves forward 2 units in a certain direction to reach point $P_{1}$, then turns left 15 degrees in the direction of motion; moves forward 2 units in the new direction to reach point $P_{2}$, then turns left 15 degrees again; moves forward 2 units in the new direction to reach point $P_{3}$, and so on.
The dot product of vectors $\overrightarrow{P_{2}P_{3}}$ and $\overrightarrow{P_{5}P_{6}}$ is $\square$. (Express as a simplified radical)