A ball is thrown from the location (x_0, y_0)=(0,0) of a horizontal...

A ball is thrown from the location $\left(x_0, y_0\right)=(0,0)$ of a horizontal playground with an initial speed $v_0$ at an angle $\theta_0$ from the $+x$-direction. The ball is to be hit by a stone, which is thrown at the same time from the location $\left(x_1, y_1\right)=(L, 0)$. The stone is thrown at an angle \left(180-\theta_1\right)$from the$+x$-direction with a suitable initial speed. For a fixed$v_0$, when \left(\theta_0, \theta_1\right)=\left(45^{\circ}, 45^{\circ}\right),$ the stone hits the ball after timeT_1, and $when \left(\theta_0, \theta_1\right)=\left(60^{\circ}, 30^{\circ}\right)$, it hits the ball after time $T_2$. In such a case, \left(T_1 / T_2\right)^2 is _______ .