` tan^ ( - 1) [ sin (( - pi ) /(2 ))] `

Explanation

` tan ^( -1) [sin (( - pi ) /(2))] `
` = tan ^( -1) [ - sin "" (pi ) /(2)], " " [ because sin ( - theta ) = -sin theta ] `
` = tan ^( -1) ( -1) , " " ( because sin "" (pi ) /(2) = 1 ) `
` = -tan ^( -1) , " " ( because tan ^( -1) (-x) = -tan ^( -1) x ) `
` = - ( pi ) /(4) , " " ( because tan ^( -1) ( 1 ) = (pi ) /(4) ) `