If the system of linear equations $(\sin\theta)x - y + z = 0$, $x - (\cos\theta)y + z = 0$, $x + y + (\sin\theta)z = 0$ has a non-trivial solution, then the least positive value of $\theta$ is
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For a homogeneous system of equations $AX = 0$, a non-trivial solution (a solution other than all variables being zero) exists only if $\det(A) = 0$. This is a fundamental concept in linear algebra.