hàm số y=(2sin2x+cos2x)/(sin2x-cos2x+3) có tất cả bao nhiêu giá trị nguyên

$\begin{array}{l}
y = \frac{{2\sin 2x + \cos 2x}}{{\sin 2x – \cos 2x + 3}}\\
\Leftrightarrow y\sin 2x – y\cos 2x + 3y = 2\sin 2x + \cos 2x\\
\Leftrightarrow \left( {y – 2} \right)\sin 2x – \left( {y + 1} \right)\cos 2x = – 3y\\
\Rightarrow pt\,\,co\,\,nghiem \Leftrightarrow {\left( {y – 2} \right)^2} + {\left( {y + 1} \right)^2} \ge 9{y^2}\\
\Leftrightarrow {y^2} – 4y + 4 + {y^2} + 2y + 1 \ge 9{y^2}\\
\Leftrightarrow 7{y^2} + 2y – 5 \le 0\\
\Leftrightarrow – 1 \le y \le \frac{5}{7}\\
y \in Z \Rightarrow y \in \left\{ { – 1;\,\,0} \right\}\\
\Rightarrow y\,\,nhan\,\,\,2\,\,gia\,\,tri\,\,nguyen.
\end{array}$