We have,cosec(75°+θ) – sec(15°-θ) - tan(55°+θ) + cot(35°-θ)

= cosec[90°-(15°-θ)] – sec(15°-θ) – tan(55°+θ) + cot[90°-(55°+θ)]

= sec(15°-θ) – sec(15°-θ) - tan(55°+θ) + tan(55°+θ)

(∵, cosec (90°- θ) = sec θ and cot(90°-θ) = tan θ)

= 0