If sin-1x+sin-1y=2pi/3 then find the value of cos-1x+cos-1y

we know that
sin^-1x = pi/2 - cos^-1x
so ​sin^-1x +​sin^-1y = 2pi/3
=> pi/2 - cos^-1x + ​pi/2 - cos^-1y= 2pi/3
=> pi - ​(cos^-1x + cos^-1y) = 2pi/3
=> ​(cos^-1x + cos^-1y) = pi-(2pi/3) = (3pi - 2pi)/3 = pi/3
so,  ​cos^-1x + cos^-1y = pi/3