Let's look at what you've found:
[MATH]\d{y}{x}=a\sin(2ax)[/MATH]
Now, we're told to let:
[MATH]\d{y}{x}=1[/MATH]
[MATH]x=\frac{\pi}{4}[/MATH]
And so we have:
[MATH]1=a\sin\left(2a\frac{\pi}{4}\right)[/MATH]
[MATH]1=a\sin\left(a\frac{\pi}{2}\right)[/MATH]
At this point, we should recognize that if \(a\in\mathbb{Z}\) then \(a\) must be odd (if it's even the sine function is zero), so let:
[MATH]a=2k+1[/MATH] where \(k\in\mathbb{Z}\)
[MATH]1=(2k+1)\sin\left((2k+1)\frac{\pi}{2}\right)[/MATH]
Now, the sine function is only going to be \(\pm1\) and so the coefficient must be the same value. What can we then conclude about \(a\)?