<s>[INST] If $\sin^2 \theta + 2\cos \theta – 2 = 0$, then find the value of $\cos^3 \theta + \sec^3 \theta$ If $\sin^2 \theta + 2\cos \theta – 2 = 0$, then find the value of $\cos^3 \theta + \sec^3 \theta$.
 [/INST] HINT:
We have $$1-\cos^2\theta+2\cos\theta-2=0\iff(\cos\theta-1)^2=0$$

Alternatively ,  $$1-\cos^2\theta+2\cos\theta-2=0\iff\cos^2\theta+1=2\cos\theta$$
Dividing by $\displaystyle\cos\theta$ (which is clearly $\ne0$)  $$\cos\theta+\sec\theta=2$$
Can you calculate $$\cos^3\theta+\sec^3\theta=\cos^3\theta+\frac1{\cos^3\theta}$$ from here?
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