Using the R method for finding all solutions to $\sin(2a) - \cos(2a) = \frac{\sqrt{6}}{2}$. My solution differs from official answer. 
How many solutions does
  $$\sin(2a) - \cos(2a) = \frac{\sqrt{6}}{2}$$ 
  have between $-90^\circ$ and $90^\circ$? 

I used the R method and got
$$2a-45^\circ = \arcsin\left(\frac{\sqrt{3}}{2}\right).$$ 
Since $a$ is between $-90^\circ$ and $90^\circ$, then $2a$ is between $-180^\circ$ and $180^\circ$. The RHS can be $60^\circ$, $120^\circ$, $-240^\circ$, and $-300^\circ$. Only $60^\circ$ and $120^\circ$ fit the criteria, but the answer is 4 solutions. 

Where did I go wrong?


You are right. Here is the image of the function using google.

