ITA 2025 (2ª fase) — Questão 3

Sejam $\alpha, \beta \in \left[\dfrac{\pi}{2}, \dfrac{3\pi}{2}\right]$ tais que

$\operatorname{sen}(\alpha) - \operatorname{sen}(\beta) = \frac{1}{4} \quad \text{e} \quad \operatorname{sen}(\alpha) - 2\operatorname{sen}(\beta) + \cos(\beta) = \frac{3}{4}.$

Calcule o valor de $\operatorname{sen}(\alpha + \beta)$.