$2 \pi-\left(\sin ^{-1} \frac{4}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{16}{65}\right)$ is equal to

If two sides of a square are $4 x+3 y-20=0$ and $4 x+3 y+15=0$, then the area of the square is

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq.m) of the flowerbed is

Let $a, b, c$ be three non-zero real numbers such that the equation $\sqrt{3} \mathrm{a} \cos x+2 b \sin x=c$, $x \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ has two distinct real roots $\alpha$ and $\beta$ with $\alpha+\beta=\frac{\pi}{3}$. Then the value of $\frac{b}{a}$ is