A ball of mass 10 kg moving with a velocity $10 \sqrt{3} \mathrm{~ms}^{-1}$ along $X$-axis, hits another ball of mass 20 kg which is at rest. After 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 $10 \mathrm{~m} / \mathrm{s}$. The second piece starts moving at a speed of $20 \mathrm{~m} / \mathrm{s}$ at an angle $\theta$ (degree) with respect to the X-axis.
The configuration of pieces after collision is shown in the figure. The value of $\theta$ to the nearest integer is $\_\_\_\_$ .