We know that Sum of eigen values = trace of the matrix
Here $\lambda_{1}+\lambda _{2}+\lambda _{3}= \sqrt{2}+1$
$1+2 \ cos\ t= \sqrt{2}+1$
$2 \ cos\ t= \sqrt{2}$
$cos \ t = \frac{1}{\sqrt{2}}$
$t = cos^{-1}(\frac{1}{\sqrt{2}})$
$t=\{-\frac{\pi}{4},\frac{\pi}{4}\}$
Hence,Option(C)$\{-\frac{\pi}{4},\frac{\pi}{4}\}$.