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[tex]3 \cos {}^{4} ( \beta ) + 6 \sin {}^{2} ( \beta ) \cos {}^{2} ( \beta ) + 3 \sin {}^{4} ( \beta ) [/tex]
[tex]3 \cos {}^{4} ( \beta ) + 6 \sin {}^{2} ( \beta ) \cos {}^{2} ( \beta ) + 3 \sin {}^{4} ( \beta ) [/tex]
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[tex]\displaystyle\bf\\3Cos^{4} \beta +6Sin^{2} \beta Cos^{2} \beta +3Sin^{4} \beta =3\cdot\Big(Cos^{4} \beta +2Sin^{2} \beta Cos^{2} \beta +Sin^{4} \beta\Big)=\\\\=3\cdot\Big(\underbrace{Cos^{2} \beta +Sin^{2} \beta}_{1} \Big)^{2} =3\cdot 1=\boxed3[/tex]