The axes of a coordinate system $$S_2$$ are inclined at an angle $$\theta$$ to those of another coordinate system $$S_1$$. The origins of both the systems are coinciding. A particle $$P_1$$ at rest in system $$S_1$$ starts from point $$(-2,0)$$ and travels along positive direction of $$X_1$$ axis with uniform acceleration of $$1.25\,\mathrm{m/s^2}$$ for 4 s and stops. In system $$S_2$$, particle $$P_2$$ starts from rest from the origin and travels for 2 s along positive direction of $$X_2$$ axis with uniform acceleration $$5\,\mathrm{m/s^2}$$ and stops. If the final distance between $$P_1$$ and $$P_2$$ is 6 m, then the angle between $$+Y_1$$ axis and $$+X_2$$ axis is