Answer
$84^{\circ}; 276^{\circ}$
Work Step by Step
Using degree mode and inverse cosine function, we get
$\theta=\cos^{-1}0.10452846=84^{\circ}$
Another possible value of $\theta$ can be found by using the identity $\cos(360^{\circ}-x)=\cos x$
$\implies \cos 84^{\circ}=\cos(360-84)^{\circ}=\cos 276^{\circ}$
$\implies\cos^{-1}0.10452846=84^{\circ}$ or $\cos^{-1}0.10452846=276^{\circ}$
