A 78-118 GHz synthesizer-driven backward-wave oscillator is used together with klystron sources and frequency doublers to measure the electric-resonance optothermal spectrum of the K(a) = 1 <-- 0 rotation-tunnelling subband of (D2O)2. Transitions are observed originating from each of the six tunnelling states, A1+, B1+, E1+, A2-, B2-, and E2-, allowing an estimate of the largest tunnelling matrix element h4v, characterizing the separation of the A1+, B1+, and E1+ states from the A2-, B2-, and E2- states. We find the average of h4v for the K(a) = 0 and 1 states to be approximately -8943 MHz. A comparison of the K(a) = 1 <-- 0 band origins for the A/B states with the band origin for their E partner gives h2v approximately -6.9 MHz, where h2v is the tunnelling matrix element responsible for the displacement of the E symmetry levels from the center of their interconversion split A/B partners. Values found for the A rotational constant, A approximately 124923 MHz, and h2v are in good agreement with those obtained from the submillimetre measurements of Zwart, E., ter Meulen, J. J., and Meerts, W. L., 1990, Chem. Phys. Lett., 173, 115, on the K(a) = 2 <-- 1 band of the complex. Estimates are presented for the potential barriers to the 1 --> 2, 1 --> 5 and 1 --> 7 tunnelling processes.