Answer
$-\dfrac {\pi }{6}$
Work Step by Step
$sec\alpha =csc\theta \Rightarrow \alpha +\theta =\dfrac {\pi }{2}\Rightarrow secx=csc\dfrac {2\pi }{3}\Rightarrow x+\dfrac {2\pi }{3}=\dfrac {\pi }{2}\Rightarrow x=-\dfrac {\pi }{6}$
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