Given that \(\sin \frac { \pi } { 3 } = \cos \frac { \pi } { k }\), state the value of the integer \(k\).
Hence, or otherwise, find the general solution of the equation
$$\cos \left( 2 x - \frac { 5 \pi } { 6 } \right) = \sin \frac { \pi } { 3 }$$
giving your answer, in its simplest form, in terms of \(\pi\).
Hence, given that \(\cos \left( 2 x - \frac { 5 \pi } { 6 } \right) = \sin \frac { \pi } { 3 }\), show that there is only one finite value for \(\tan x\) and state its exact value. [0pt]
[2 marks]