$f(x)=\sec ^{-1} \frac{2 x}{5 x+3}$
$\left|\frac{2 x}{5 x+3}\right|$

$\left|\frac{2 x}{5 x+3}\right| \geq 1 \Rightarrow|2 x| \geq|5 x+3|$

$(2 x)^2-(5 x+3)^2 \geq|5 x+3|$

$(7 x+3)(-3 x-3) \geq 0$

$\frac{-\quad-\quad-}{-1} \quad-\frac{3}{7}$

$\text { domain }\left[-1, \frac{-3}{5}\right) \cup\left(\frac{-3}{5}, \frac{-3}{7}\right]$

$\alpha=-1, \beta=\frac{-3}{5}, \gamma=\frac{-3}{5}, \delta=\frac{-3}{7}$

$3 \alpha+10(\beta+\gamma)+21 \delta=-3$

$-3+10\left(\frac{-6}{5}\right)+\left(\frac{-3}{7}\right) 21=-24$