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Let lambda and alpha be real. Find the s...

Let `lambda` and `alpha` be real. Find the set of all values of `lambda` for which the system of linear equations
`lambdax + ("sin"alpha)y + ("cos" alpha)z =0`,
`x + ("cos"alpha)y + ("sin" alpha) z =0`
and `-x + ("sin" alpha)y -("cos" alpha)z =0`
has a non-trivial solution.
For `lambda =1`, find all values of `alpha`.

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