Determinants question bank (Maths)

The sum of all possible values of $\theta \in [0, 2\pi]$, for which the system of equations :
$x\cos 3\theta - 8y - 12z = 0$
$x\cos 2\theta + 3y + 3z = 0$
$x + y + 3z = 0$
has a non-trivial solution, is equal to :

If $f: \mathbf{N} \rightarrow \mathbf{Z}$ is defined by
$f(n) = \begin{vmatrix} n & -1 & -5 \\ -2n^2 & 3(2k+1) & 2k+1 \\ -3n^3 & 3k(2k+1) & 3k(k+2)+1 \end{vmatrix}$, $k \in \mathbf{N}$,
and $\sum_{n=1}^{k} f(n) = 98$, then $k$ is equal to :