Question 98
Let $\alpha, \beta, \gamma \in [0; \frac{\pi}{2}]$ satisfy the conditions
$$
\sin \alpha + \sin \beta + \sin \gamma = 1, \sin \alpha \cos 2\alpha + \sin \beta \cos 2\beta + \sin \gamma \cos 2\gamma = -1.
$$
Find all the possible values of the expression $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma$.
$$
\sin \alpha + \sin \beta + \sin \gamma = 1, \sin \alpha \cos 2\alpha + \sin \beta \cos 2\beta + \sin \gamma \cos 2\gamma = -1.
$$
Find all the possible values of the expression $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma$.