Let \( \lambda \) and \( \alpha \) be real. Find the set of all val...

Let \( \lambda \) and \( \alpha \) be real. Find the set of all values of \( \lambda \) for which the system of linear equations
\[
\begin{aligned}
\lambda x+(\sin \alpha) y+(\cos \alpha) z &=0 \\
x+(\cos \alpha) y+(\sin \alpha) z &=0 \\
-x+(\sin \alpha) y-(\cos \alpha) z &=0
\end{aligned}
\]
and
has a non-trivial solution.
For \( \lambda=1 \), find all values of \( \alpha \).
\( (1993,5 \mathrm{M}) \)