cosø=tanø=sinø/cosø; cos^2ø=sinø; 1-sin^2ø=sinø; sin^2ø+sinø=1; sin^2ø+sinø+1/4=5/4; (sinø+1/2)^2=5/4.
sinø+0.5=+sqrt(5)/2; ø=arcsin(+sqrt(5)/2-0.5)=38.173 degrees. Also 141.827 degrees (180-38.173). The negative square root gives a sine value out of range. [The sine of this angle involves the Golden Ratio: 0.618034 (approx) because 1.618034=1/0.618034, the solution of the equation 1+x=1/x. x is sinø in this question: 1+sinø=1/sinø.]