Solve the equation \(\operatorname { cosec } \theta = - 4\) for \(0 ^ { \circ } < \theta < 360 ^ { \circ }\), giving your answers to the nearest \(0.1 ^ { \circ }\).
Solve the equation
$$2 \cot ^ { 2 } \left( 2 x + 30 ^ { \circ } \right) = 2 - 7 \operatorname { cosec } \left( 2 x + 30 ^ { \circ } \right)$$
for \(0 ^ { \circ } < x < 180 ^ { \circ }\), giving your answers to the nearest \(0.1 ^ { \circ }\).
Describe a sequence of two geometrical transformations that maps the graph of \(y = \operatorname { cosec } x\) onto the graph of \(y = \operatorname { cosec } \left( 2 x + 30 ^ { \circ } \right)\).