A ball of mass $10 \mathrm{kg}$ moving with a velocity $10\sqrt{3}{ \mathrm{m} \mathrm{s}}^{-1}$ along $X$-axis, hits another ball of mass $20 \mathrm{kg}$ which is at rest. After the collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along $Y$-axis at a speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$. The second piece starts moving at a speed of $20 \mathrm{m} {\mathrm{s}}^{-1}$ at an angle $\theta$ (degree) with respect to the $X$-axis. The configuration of pieces after the collision is shown in the figure. The value of $\theta$ to the nearest integer is _________.