$ = {\sin ^2}\alpha + \cos (\alpha + \beta )\{ \cos (\alpha + \beta ) + 2\sin \alpha \sin \beta \} $
$ = {\sin ^2}\alpha + \cos (\alpha + \beta )\cos (\alpha - \beta )$
$ = {\sin ^2}\alpha + \frac{1}{2}(\cos 2\alpha + \cos 2\beta )$
$ = {\sin ^2}\alpha + {\cos ^2}\alpha - \frac{1}{2} + \frac{{\cos 2\beta }}{2}$
==> $y = $ constant ==> $\frac{{{d^3}y}}{{d{\alpha ^3}}} = 0$
Trick: Let $\beta = 180^\circ $ { since $\beta $ is constant}
$\therefore y = {\sin ^2}\alpha + {\cos ^2}\alpha = 1 \Rightarrow \frac{{{d^3}y}}{{d{\alpha ^3}}} = 0$.
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