Find the value of cot 2 60° + sin 2 45° + tan 2 30° + 3/2

 cot ² 60° + sin ² 45° + tan ² 30° + \(\frac{3}{2}\)

=   (\(\frac{1}{\sqrt {3}}\))²   (\(\frac{1}{\sqrt {2}}\))²  + (\(\frac{1}{\sqrt {3}}\))²  +  \(\frac{3}{2}\)

=   \(\frac{1}{3}\) + \(\frac{1}{2}\) +  \(\frac{1}{3}\)  +  \(\frac{3}{2}\)

=  \(\frac{2 + 3 + 2 + 9  }{6}\) =  \(\frac{16}{6}\)=  \(\frac{8}{3}\)