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\( \mathrm{L}_{1} \) and \( \mathrm{L}_{2} \) are two lines whose vector equations are
\[
\begin{array}{l}
L_{1}: \overrightarrow{\mathrm{r}}=\lambda[(\cos \theta+\sqrt{3}) \hat{\mathrm{i}}+(\sqrt{2} \sin \theta) \hat{\mathrm{j}}+(\cos \theta-\sqrt{3}) \hat{\mathrm{k}}] \\
\mathrm{L}_{2}: \overrightarrow{\mathrm{r}}=\mu(\hat{\mathrm{i}}+\mathrm{bj}+\mathrm{j} \hat{\mathrm{k}}),
\end{array}
\]
P
W
where \( \lambda \) and \( \mu \) are scalars and \( \alpha \) is the acute angle between \( \mathrm{L}_{1} \) and \( \mathrm{L}_{2} \). If the angle \( \alpha \) is independent of \( \theta \) then the value of \( \alpha \) is
(A) \( \frac{\pi}{6} \)
(B) \( \frac{\pi}{4} \)
(C) \( \frac{\pi}{3} \)
(D) \( \frac{\pi}{2} \)
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