6 Anna has been asked to describe the transformation given by the matrix $$\left[ \begin{array} { c c c } 1 & 0 & 0
0 & - \frac { \sqrt { 3 } } { 2 } & - \frac { 1 } { 2 }
0 & \frac { 1 } { 2 } & - \frac { \sqrt { 3 } } { 2 } \end{array} \right]$$ She writes her answer as follows: The transformation is a rotation about the \(x\)-axis through an angle of \(\theta\), where $$\begin{gathered} \sin \theta = \frac { 1 } { 2 } \quad \text { and } \quad - \sin \theta = - \frac { 1 } { 2 }
\theta = 30 ^ { \circ } \end{gathered}$$ Identify and correct the error in Anna's work.
[0pt] [2 marks]
\(7 \quad\) Prove by induction that, for all integers \(n \geq 1\), the expression \(7 ^ { n } - 3 ^ { n }\) is divisible by 4