Given sec(theta)(sin(theta)>0 => cos(theta)sin(theta)>0 => cos(theta) and sin(theta) have the same sign, => sin(theta)<0 => theta is in the third quadrant. => tan(theta)>0
Given cos(theta)=-0.96 => |sin(theta)|=sqrt(1-(-0.96)^2)=sqrt(0.0784)=0.28 => sin(theta)=-0.28
Finally, tan(theta)=sin(theta)/cos(theta)=-0.28/-0.96 =7/24 =0.29167 (to the fifth decimal place)