Solve the trigonometric equations on the interval $0\le \theta <2\pi $.

(32)$4(1+\mathrm{sin}\theta )={\mathrm{cos}}^{2}\theta $

(38)$\mathrm{sec}\theta =\mathrm{tan}\theta +\mathrm{cot}\theta $

(40)$\sqrt{3}\mathrm{sin}\theta +\mathrm{cos}\theta =1$

(32)$4(1+\mathrm{sin}\theta )={\mathrm{cos}}^{2}\theta $

(38)$\mathrm{sec}\theta =\mathrm{tan}\theta +\mathrm{cot}\theta $

(40)$\sqrt{3}\mathrm{sin}\theta +\mathrm{cos}\theta =1$