Hi,
Convert that expression into R+I*j using two applications of your known conversion to sin and cos, then multiply the denominator of the fraction by the complex conjugate of what you find. That gives you a form that looks like N/D where N might be complex and D is always real, then dividing each part of N by D you get a single complex number in the form Real+Imag*j. The complex absolute value is the front multiplier, and the complex part is inside the cos() function, then use the two argument inverse tangent function to get the phase shift from that complex part (dont use the single argument inverse tangent function).