Answer
$\dfrac {9}{4}+\sqrt {2} $
Work Step by Step
$\left( \sin \dfrac {\pi }{3}\tan \dfrac {\pi }{6}+csc\dfrac {\pi }{4}\right) ^{2}=\left( \dfrac {\sin \dfrac {\pi }{3}\times \sin \dfrac {\pi }{6}}{\cos \dfrac {\pi }{6}}+\dfrac {1}{\sin \dfrac {\pi }{4}}\right) ^{2}=\left( \dfrac {\dfrac {\sqrt {3}}{2}\times \dfrac {1}{2}}{\dfrac {\sqrt {3}}{2}}+\dfrac {1}{\dfrac {\sqrt {2}}{2}}\right) ^{2}=\left( \dfrac {1}{2}+\sqrt {2}\right) ^{2}==\dfrac {1}{4}+2\times \dfrac {1}{2}\times \sqrt {2}+2=\dfrac {9}{4}+\sqrt {2} $
