Show that the equation \(4 \operatorname { cosec } ^ { 2 } \theta - \cot ^ { 2 } \theta = k\), where \(k \neq 4\), can be written in the form
$$\sec ^ { 2 } \theta = \frac { k - 1 } { k - 4 }$$
Hence, or otherwise, solve the equation
$$4 \operatorname { cosec } ^ { 2 } \left( 2 x + 75 ^ { \circ } \right) - \cot ^ { 2 } \left( 2 x + 75 ^ { \circ } \right) = 5$$
giving all values of \(x\) in the interval \(0 ^ { \circ } < x < 180 ^ { \circ }\). [0pt]
[5 marks]
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