If $\alpha, \beta, \gamma$ are angles of a triangle,then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma - 2 \cos \alpha \cos \beta \cos \gamma$ is

Statement-$I$: In the interval $[0, 2\pi]$,the number of common solutions of the equations $2 \sin^2 \theta - \cos 2\theta = 0$ and $2 \cos^2 \theta - 3 \sin \theta = 0$ is two.
Statement-$II$: The number of solutions of $2 \cos^2 \theta - 3 \sin \theta = 0$ in $[0, \pi]$ is two.

In $\triangle ABC$,$(a-b)^2 \sin^2\left(\frac{A+B}{2}\right) + (a+b)^2 \sin^2\left(\frac{C}{2}\right) = $

If in $\Delta ABC$,$2b^2 = a^2 + c^2$,then $\frac{\sin 3B}{\sin B} = $

In a triangle $ABC$,angle $A$ is greater than angle $B$. If the measures of angles $A$ and $B$ satisfy the equation $3\sin x - 4\sin^3 x - k = 0$ for $0 < k < 1$,then the measure of angle $C$ is:

Let $S = \{\theta \in (0, 2\pi) : 7 \cos^2 \theta - 3 \sin^2 \theta - 2 \cos^2 2\theta = 2\}$. Then,the sum of roots of all the equations $x^2 - 2(\tan^2 \theta + \cot^2 \theta)x + 6 \sin^2 \theta = 0$ for $\theta \in S$ is...