Find the general solution of the equation
$$\cos \left( \frac { 5 } { 4 } x - \frac { \pi } { 3 } \right) = \frac { \sqrt { 2 } } { 2 }$$
giving your answer for \(x\) in terms of \(\pi\).
Use your general solution to find the sum of all the solutions of the equation \(\cos \left( \frac { 5 } { 4 } x - \frac { \pi } { 3 } \right) = \frac { \sqrt { 2 } } { 2 }\) that lie in the interval \(0 \leqslant x \leqslant 20 \pi\). Give your answer in the form \(k \pi\), stating the exact value of \(k\). [0pt]
[4 marks]