The diagram shows part of the graph of \(\mathrm { y } = \operatorname { cosec } \mathrm { x }\), where \(x\) is in radians.
State the equations of the three vertical asymptotes that can be seen.
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The tangent to the graph at the point P with \(x\)-coordinate \(\frac { \pi } { 3 }\) meets the \(x\)-axis at Q .
Show that the \(x\)-coordinate of Q is \(\frac { \pi } { 3 } + \sqrt { 3 }\). (You may use without proof the result that the derivative of \(\operatorname { cosec } x\) is \(- \operatorname { cosec } x \cot x\).)