Монгол Бодлогын Сан

$(\ctg^2x+2)\sin x=\dfrac 52\Leftrightarrow \left\{ % \begin{array}{l} t=\sin x\ne 0 \\ \fbox{a}t^2-\fbox{b}t+2=0 \\ \end{array} % \right. \Leftrightarrow\\ \Leftrightarrow \left[ % \begin{array}{l} \sin x=\fbox{c}\\ \sin x=\dfrac1{\fbox{d}} \\ \end{array} % \right. \Leftrightarrow x=(-1)^k\dfrac{\pi}{\fbox{e}}+\fbox{f}k\pi, k\in \mathbb Z.$