Solve the equation \(\tan \left( x + 52 ^ { \circ } \right) = \tan 22 ^ { \circ }\), giving the values of \(x\) in the interval \(0 ^ { \circ } \leqslant x \leqslant 360 ^ { \circ }\).
Show that the equation
$$3 \tan \theta = \frac { 8 } { \sin \theta }$$
can be written as
$$3 \cos ^ { 2 } \theta + 8 \cos \theta - 3 = 0$$
Find the value of \(\cos \theta\) that satisfies the equation
$$3 \cos ^ { 2 } \theta + 8 \cos \theta - 3 = 0$$
Hence solve the equation
$$3 \tan 2 x = \frac { 8 } { \sin 2 x }$$
giving all values of \(x\) to the nearest degree in the interval \(0 ^ { \circ } \leqslant x \leqslant 180 ^ { \circ }\).