The expression $(cos^6\theta +sin^6\theta -1) (tan^2\theta +cot^2\theta +2)+1$ is equal to :

-2

(cos⁶θ + sin⁶θ - 1 ) ( tan²θ + cot²θ + 2 ) + 1

Put θ = 30º

= (  (\(\frac{√3}{2}\))⁶ + (\(\frac{1}{2}\))⁶ - 1 ) ( (\(\frac{1}{√3}\))² + (√3)² + 2 ) + 1

= ( \(\frac{27}{64}\) + \(\frac{1}{64}\) - 1 ) ( \(\frac{1}{3}\) + 3 + 2 ) + 1

= ( -\(\frac{36}{64}\)  ) ( \(\frac{16}{3}\)  + 1

= -2