The value of $$\frac{{3\left( {{{\cot }^2}{{47}^ \circ } - {{\sec }^2}{{43}^ \circ }} \right) - 2\left( {{{\tan }^2}{{23}^ \circ } - {\text{cose}}{{\text{c}}^2}{{67}^ \circ }} \right)}}{{{\text{cose}}{{\text{c}}^2}\left( {{{68}^ \circ } + \theta } \right) - \tan \left( {\theta + {{61}^ \circ }} \right) - {{\tan }^2}\left( {{{22}^ \circ } - \theta } \right) + \cot \left( {{{29}^ \circ } - \theta } \right)}}\,{\text{is:}}$$

Solution(By Examveda Team)

$$\eqalign{ & \frac{{3\left( {{{\cot }^2}{{47}^ \circ } - {{\sec }^2}{{43}^ \circ }} \right) - 2\left( {{{\tan }^2}{{23}^ \circ } - {\text{cose}}{{\text{c}}^2}{{67}^ \circ }} \right)}}{{{\text{cose}}{{\text{c}}^2}\left( {{{68}^ \circ } + \theta } \right) - \tan \left( {\theta + {{61}^ \circ }} \right) - {{\tan }^2}\left( {{{22}^ \circ } - \theta } \right) + \cot \left( {{{29}^ \circ } - \theta } \right)}} \cr & = \frac{{3\left( {{{\tan }^2}{{43}^ \circ } - {{\sec }^2}{{43}^ \circ }} \right) - 2\left( {{{\tan }^2}{{23}^ \circ } - {{\sec }^2}{{23}^ \circ }} \right)}}{{{\text{cose}}{{\text{c}}^2}\left( {{{68}^ \circ } + \theta } \right) - \tan \left( {\theta + {{61}^ \circ }} \right) - {{\cot }^2}\left( {{{68}^ \circ } - \theta } \right) + \tan \left( {{{61}^ \circ } - \theta } \right)}} \cr & = \frac{{3 \times \left( { - 1} \right) - 2 \times \left( { - 1} \right)}}{1} \cr & = \frac{{ - 3 + 2}}{1} \cr & = - 1 \cr} $$