Differential Equation involving System of Equations Find a solution to the boundary value problem \begin{align}y''+ 4y &= 0 \\ y\left(\frac{\pi}{8}\right) &=0\\
y\left(\frac{\pi}{6}\right) &= 1\end{align}
if the general solution to the differential equation is $y(x) = C_1 \sin(2x) + C_2 \cos (2x)$.
I was able to compute the following equations:
\begin{align}C_1 \left(\frac 12\right)\sqrt2 + C_2 \left(\frac 12\right)\sqrt2 &= 0\\
C_1 \left(\frac 12\right)\sqrt3 + C_2 \left(\frac 12\right) &= 1\end{align}
However I am unable to solve the system of equations. The books says the answer is $\frac{2}{\sqrt3 -1}$for $C_1$ and $-C_2$.  I am not sure how to go about manipulating the equations to get on variable. 

\begin{align*}
\frac{\sqrt 2 C_1}{2} + \frac{\sqrt 2 C_1}{2} &= 0 \\
C_1 + C_2 &= 0 \\
C_2 &= -C_1 \\
\frac{\sqrt{3}C_1}{2} + \frac{C_2}{2} &= 1 \\
\sqrt{3}C_1 + C_2 &= 2 \\
\sqrt{3}C_1 - C_1 &= 2 \\
(\sqrt{3} - 1)C_1 &= 2 \\
C_1 &= \frac{2}{(\sqrt{3} - 1)} \\
C_2 &= -\frac{2}{(\sqrt{3} - 1)} \\
\end{align*}
Which is what the book got.
