\[\begin{array}{l}
b/1 + \sin x + \cos x + \sin 2x + \cos 2x = 0\left( * \right)\\
\left( * \right) \leftrightarrow 1 + \sin x + \cos x + 2\sin x\cos x + {\cos ^2}x - {\sin ^2}x = 0\\
\leftrightarrow \left( {1 + 2\sin x\cos x} \right) + \left( {\cos x + \sin x} \right)\left( {1 + \cos x - \sin x} \right) = 0\\
\leftrightarrow {\left( {\sin x + \cos x} \right)^2} + \left( {\cos x + \sin x} \right)\left( {1 + \cos x - \sin x} \right) = 0\\
\leftrightarrow \left( {\sin x + \cos x} \right)\left( {1 + 2\cos x} \right) = 0
\end{array}\]